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Papers by Alejandro Tiraboschi

Research paper thumbnail of Automorphisms of non-singular nilpotent Lie algebras

arXiv (Cornell University), Nov 25, 2011

For a real, non-singular, 2-step nilpotent Lie algebra n, the group Aut(n)/ Aut 0 (n), where Aut ... more For a real, non-singular, 2-step nilpotent Lie algebra n, the group Aut(n)/ Aut 0 (n), where Aut 0 (n) is the group of automorphisms which act trivially on the center, is the direct product of a compact group with the 1dimensional group of dilations. Maximality of some automorphisms groups of n follows and is related to how close is n to being of Heisenberg type. For example, at least when the dimension of the center is two, dim Aut(n) is maximal if and only if n is type H. The connection with fat distributions is discussed.

Research paper thumbnail of On Slim Double Lie Groupoids

ABSTRACT. We prove that every slim double Lie groupoid with proper core action is completely dete... more ABSTRACT. We prove that every slim double Lie groupoid with proper core action is completely determined by a factorization of a certain canonically defined "diagonal " Lie groupoid.

Research paper thumbnail of NB Andersenand

Journal of Lie Theory, 2000

V. Lafforgue A proof of property (RD) for cocompact lattices of SL(3;R) and SL(3;C ) ............... more V. Lafforgue A proof of property (RD) for cocompact lattices of SL(3;R) and SL(3;C ) ................. ....... 255{267 ... D. Joyner On nite dimensional representations of non-connected reductive groups . . . . . . . . . . . . . . . . . . 269{284 ... H. Sabourin Un exemple de repr esentations unipotentes associe es a une orbite nilpotente non minimale: le cas des orbites de dimension 10 de so(4,3) . . . . . . . 285{310 ... NB Andersenand M. Unterberger Harmonic analysis on SU(n; n)=SL(n;C ) R+. .... 311{322 ... EA Tevelev On the Chevalley restriction theorem . . . . . . . . . . . . . 323{330

Research paper thumbnail of Quasi-Lie bialgebras with quasi-triangular decomposition

Journal of Lie Theory, 2000

Journal of Lie Theory, Vol. 10, No. 2, pp. 383-397 (2000) Quasi-Lie bialgebras with quasi-triangu... more Journal of Lie Theory, Vol. 10, No. 2, pp. 383-397 (2000) Quasi-Lie bialgebras with quasi-triangular decomposition. Nicolás Andruskiewitsch and Alejandro Tiraboschi. FAMAF Universidad Nacional de Córdoba Ciudad Universitaria (5000) Córdoba Argentina andrus@famaf.unc.edu.ar tirabo@famaf.unc.edu.ar. Abstract: A class of Lie bialgebras and quasi-Lie bialgebras related to a triangular decomposition of the underlying Lie algebras is discussed. New examples are presented. ...

Research paper thumbnail of Lie quasi-bialgebras with quasi-triangular decomposition

Journal of Lie theory

ABSTRACT

Research paper thumbnail of Regular Metabelian Lie Algebras

Geometry and Representation Theory of Real and p-adic groups, 1996

Research paper thumbnail of On gelfand-kirillov dimensions ( g,A ) of modules

Communications in Algebra, 1992

Let Gbe a real connected semisimple real Lie group and let be Aa connected reductive subgroupg,at... more Let Gbe a real connected semisimple real Lie group and let be Aa connected reductive subgroupg,athe complexified Lie algebras of Gand A respectively; assume (g,a) is a regular pair.In this paper we study general properties of (g, A)-modules, and we prove for two particular cases that every admissible (g, A)-module with an infinitesimal character has finite length.We also compute Gelfand-Kiriilov

Research paper thumbnail of On slim double Lie groupoids

We prove that every slim double Lie groupoid with proper core action is completely determined by ... more We prove that every slim double Lie groupoid with proper core action is completely determined by a factorization of a certain canonically defined "diagonal" Lie groupoid.

Research paper thumbnail of A family of Poisson non-compact symmetric spaces

We study Poisson symmetric spaces of group type with Cartan subalgebra "adapted" to the Lie cobra... more We study Poisson symmetric spaces of group type with Cartan subalgebra "adapted" to the Lie cobracket.

Research paper thumbnail of Quantum Heisenberg groups and sklyanin algebras

Letters in Mathematical Physics, 1994

New bialgebra structures on the Heisenberg-Lie algebra and their quantizations are introduced. So... more New bialgebra structures on the Heisenberg-Lie algebra and their quantizations are introduced. Some of these quantizations give rise to new multiplications in homogeneous coordinate rings of Abelian varieties, via the well-known identification of theta functions with suitable matrix coefficients of the Stone-von Neumann representations.

Research paper thumbnail of A family of Poisson non-compact symmetric spaces

Journal of Geometry and Physics, 2010

Research paper thumbnail of Horizontal submanifolds of groups of Heisenberg type

Annali Di Matematica Pura Ed Applicata, 2008

We study maximal horizontal subgroups of Carnot groups of Heisenberg type. We classify those of d... more We study maximal horizontal subgroups of Carnot groups of Heisenberg type. We classify those of dimension half of that of the canonical distribution (“lagrangians”) and illustrate some notable ones of small dimension. An infinitesimal classification of the arbitrary maximal horizontal submanifolds follows as a consequence.

Research paper thumbnail of Poisson Algebras of Spinor Functions

Poisson algebras of spinor-valued functions arise as we extend the classical Hamiltonian formalis... more Poisson algebras of spinor-valued functions arise as we extend the classical Hamiltonian formalism to vector-valued symplectic forms. ISSN 0949-5932 / $2.50 c Heldermann Verlag 66

Research paper thumbnail of Classes of 2-step nilpotent lie algebras

Communications in Algebra, 1999

Research paper thumbnail of Horizontal submanifolds of groups of Heisenberg type

We study maximal horizontal subgroups of Carnot groups of Heisenberg type. We classify those of d... more We study maximal horizontal subgroups of Carnot groups of Heisenberg type. We classify those of dimension half of that of the canonical distribution ("lagrangians") and illustrate some notable ones of small dimension. An infinitesimal classification of the arbitrary maximal horizontal submanifolds follows as a consequence.

Research paper thumbnail of Multiplier Infinitesimal Bialgebras and Derivator Lie Bialgebras

We propose a definition of multiplier infinitesimal bialgebra and a definition of derivator Lie b... more We propose a definition of multiplier infinitesimal bialgebra and a definition of derivator Lie bialgebra. We give some examples of these structures and prove that every bibalanced multiplier infinitesimal bialgebra gives rise to a multiplier Lie bialgebra.

Research paper thumbnail of Automorphisms of Non-Singular Nilpotent Lie Algebras

For a real, non-singular, 2-step nilpotent Líe algebra n, the group Aut(n)/ Auto(n), where Auto(n... more For a real, non-singular, 2-step nilpotent Líe algebra n, the group Aut(n)/ Auto(n), where Auto(n) is the group of automorphisms which act trivially on the center, is the direct product of a compact group with the l-dimensional group of dilations. Maximality of some automorphísms groups of n follows and is related to how close is n to being of Heisenberg type. For example, at least when the dimension ofthe center is two, dimAut(n) is maximal if and only if n is of Heisenberg type. The connection with fat distributions is discussed. Matbematics Subject Classification 2010: 17B30, 16W25.

Research paper thumbnail of Automorphisms of non-singular nilpotent Lie algebras

arXiv (Cornell University), Nov 25, 2011

For a real, non-singular, 2-step nilpotent Lie algebra n, the group Aut(n)/ Aut 0 (n), where Aut ... more For a real, non-singular, 2-step nilpotent Lie algebra n, the group Aut(n)/ Aut 0 (n), where Aut 0 (n) is the group of automorphisms which act trivially on the center, is the direct product of a compact group with the 1dimensional group of dilations. Maximality of some automorphisms groups of n follows and is related to how close is n to being of Heisenberg type. For example, at least when the dimension of the center is two, dim Aut(n) is maximal if and only if n is type H. The connection with fat distributions is discussed.

Research paper thumbnail of On Slim Double Lie Groupoids

ABSTRACT. We prove that every slim double Lie groupoid with proper core action is completely dete... more ABSTRACT. We prove that every slim double Lie groupoid with proper core action is completely determined by a factorization of a certain canonically defined "diagonal " Lie groupoid.

Research paper thumbnail of NB Andersenand

Journal of Lie Theory, 2000

V. Lafforgue A proof of property (RD) for cocompact lattices of SL(3;R) and SL(3;C ) ............... more V. Lafforgue A proof of property (RD) for cocompact lattices of SL(3;R) and SL(3;C ) ................. ....... 255{267 ... D. Joyner On nite dimensional representations of non-connected reductive groups . . . . . . . . . . . . . . . . . . 269{284 ... H. Sabourin Un exemple de repr esentations unipotentes associe es a une orbite nilpotente non minimale: le cas des orbites de dimension 10 de so(4,3) . . . . . . . 285{310 ... NB Andersenand M. Unterberger Harmonic analysis on SU(n; n)=SL(n;C ) R+. .... 311{322 ... EA Tevelev On the Chevalley restriction theorem . . . . . . . . . . . . . 323{330

Research paper thumbnail of Quasi-Lie bialgebras with quasi-triangular decomposition

Journal of Lie Theory, 2000

Journal of Lie Theory, Vol. 10, No. 2, pp. 383-397 (2000) Quasi-Lie bialgebras with quasi-triangu... more Journal of Lie Theory, Vol. 10, No. 2, pp. 383-397 (2000) Quasi-Lie bialgebras with quasi-triangular decomposition. Nicolás Andruskiewitsch and Alejandro Tiraboschi. FAMAF Universidad Nacional de Córdoba Ciudad Universitaria (5000) Córdoba Argentina andrus@famaf.unc.edu.ar tirabo@famaf.unc.edu.ar. Abstract: A class of Lie bialgebras and quasi-Lie bialgebras related to a triangular decomposition of the underlying Lie algebras is discussed. New examples are presented. ...

Research paper thumbnail of Lie quasi-bialgebras with quasi-triangular decomposition

Journal of Lie theory

ABSTRACT

Research paper thumbnail of Regular Metabelian Lie Algebras

Geometry and Representation Theory of Real and p-adic groups, 1996

Research paper thumbnail of On gelfand-kirillov dimensions ( g,A ) of modules

Communications in Algebra, 1992

Let Gbe a real connected semisimple real Lie group and let be Aa connected reductive subgroupg,at... more Let Gbe a real connected semisimple real Lie group and let be Aa connected reductive subgroupg,athe complexified Lie algebras of Gand A respectively; assume (g,a) is a regular pair.In this paper we study general properties of (g, A)-modules, and we prove for two particular cases that every admissible (g, A)-module with an infinitesimal character has finite length.We also compute Gelfand-Kiriilov

Research paper thumbnail of On slim double Lie groupoids

We prove that every slim double Lie groupoid with proper core action is completely determined by ... more We prove that every slim double Lie groupoid with proper core action is completely determined by a factorization of a certain canonically defined "diagonal" Lie groupoid.

Research paper thumbnail of A family of Poisson non-compact symmetric spaces

We study Poisson symmetric spaces of group type with Cartan subalgebra "adapted" to the Lie cobra... more We study Poisson symmetric spaces of group type with Cartan subalgebra "adapted" to the Lie cobracket.

Research paper thumbnail of Quantum Heisenberg groups and sklyanin algebras

Letters in Mathematical Physics, 1994

New bialgebra structures on the Heisenberg-Lie algebra and their quantizations are introduced. So... more New bialgebra structures on the Heisenberg-Lie algebra and their quantizations are introduced. Some of these quantizations give rise to new multiplications in homogeneous coordinate rings of Abelian varieties, via the well-known identification of theta functions with suitable matrix coefficients of the Stone-von Neumann representations.

Research paper thumbnail of A family of Poisson non-compact symmetric spaces

Journal of Geometry and Physics, 2010

Research paper thumbnail of Horizontal submanifolds of groups of Heisenberg type

Annali Di Matematica Pura Ed Applicata, 2008

We study maximal horizontal subgroups of Carnot groups of Heisenberg type. We classify those of d... more We study maximal horizontal subgroups of Carnot groups of Heisenberg type. We classify those of dimension half of that of the canonical distribution (“lagrangians”) and illustrate some notable ones of small dimension. An infinitesimal classification of the arbitrary maximal horizontal submanifolds follows as a consequence.

Research paper thumbnail of Poisson Algebras of Spinor Functions

Poisson algebras of spinor-valued functions arise as we extend the classical Hamiltonian formalis... more Poisson algebras of spinor-valued functions arise as we extend the classical Hamiltonian formalism to vector-valued symplectic forms. ISSN 0949-5932 / $2.50 c Heldermann Verlag 66

Research paper thumbnail of Classes of 2-step nilpotent lie algebras

Communications in Algebra, 1999

Research paper thumbnail of Horizontal submanifolds of groups of Heisenberg type

We study maximal horizontal subgroups of Carnot groups of Heisenberg type. We classify those of d... more We study maximal horizontal subgroups of Carnot groups of Heisenberg type. We classify those of dimension half of that of the canonical distribution ("lagrangians") and illustrate some notable ones of small dimension. An infinitesimal classification of the arbitrary maximal horizontal submanifolds follows as a consequence.

Research paper thumbnail of Multiplier Infinitesimal Bialgebras and Derivator Lie Bialgebras

We propose a definition of multiplier infinitesimal bialgebra and a definition of derivator Lie b... more We propose a definition of multiplier infinitesimal bialgebra and a definition of derivator Lie bialgebra. We give some examples of these structures and prove that every bibalanced multiplier infinitesimal bialgebra gives rise to a multiplier Lie bialgebra.

Research paper thumbnail of Automorphisms of Non-Singular Nilpotent Lie Algebras

For a real, non-singular, 2-step nilpotent Líe algebra n, the group Aut(n)/ Auto(n), where Auto(n... more For a real, non-singular, 2-step nilpotent Líe algebra n, the group Aut(n)/ Auto(n), where Auto(n) is the group of automorphisms which act trivially on the center, is the direct product of a compact group with the l-dimensional group of dilations. Maximality of some automorphísms groups of n follows and is related to how close is n to being of Heisenberg type. For example, at least when the dimension ofthe center is two, dimAut(n) is maximal if and only if n is of Heisenberg type. The connection with fat distributions is discussed. Matbematics Subject Classification 2010: 17B30, 16W25.