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Papers by Jorge Andrés Devoto
Unknown, 1991
We study the modular properties of a formal power series of elliptic operators that correspond to... more We study the modular properties of a formal power series of elliptic operators that correspond to the S (sup 1)-equivariant index of a hypothetical Dirac operator on loop spaces of a manifold twisted by the action of a group. We also show that this interpretation ...
AIP Conference Proceedings, 2006
We study, for Γ a discrete group of finite virtual cohomological dimension the elliptic cohomolog... more We study, for Γ a discrete group of finite virtual cohomological dimension the elliptic cohomology of the classifying space BΓ.
We present an overview of elliptic cohomology and equivariant elliptic cohomology, emphasizing it... more We present an overview of elliptic cohomology and equivariant elliptic cohomology, emphasizing its relations with some classical results of the cohomology and K-theory of classifying spaces of finite groups. Finally we make some remarks about the relevance of elliptic cohomology for the “Monster moonshine” phenomena.
DESCRIPTION We show that if MMM is a Frobenius manifold of dimension nnn such that TxMT_{x} MTxM is s... more DESCRIPTION We show that if MMM is a Frobenius manifold of dimension nnn such that TxMT_{x} MTxM is semisimple for every xinMx \in MxinM, then there exists a canonical 2-vector bundle mathcalB\mathcal{B}mathcalB over MMM of rank nnn. This 2-vector bundle encodes the information about the maximal category of DDD-branes associated to the open closed topological field theories defined by the Frobenius algebras TxMT_{x} MTxM. In particular this construction answers a conjecture of Graeme Segal in~\cite{segal07:_what_is_ellip_objec}. We also explain the relation of the labels of the DDD-branes to Azumaya algebras and twisted vector bundles on the spectral cover SSS of MMM.
Michigan Mathematical Journal, 1996
Letters in Mathematical Physics, 1994
We define new quantizations of the Heisenberg group by introducing new quantizations in the unive... more We define new quantizations of the Heisenberg group by introducing new quantizations in the universal enveloping algebra of its Lie algebra. Matrix coefficients of the Stone-von Neumann representation are preserved by these new multiplications on the algebra of functions on the Heisenberg group. Some of the new quantizations provide also a new multiplication in the algebra of theta functions; we obtain in this way Sklyanin algebras.
Journal of Pure and Applied Algebra, 1998
Let G be a finite group of order (GI odd and let 6Y~*(-)~?@[l/lGl] denote elliptic cohomology ten... more Let G be a finite group of order (GI odd and let 6Y~*(-)~?@[l/lGl] denote elliptic cohomology tensored by Z[l/lGl]. Then we give a description of &Y*(E(N,G) x ,vX) @ Z[l/lGl], where N is a normal subgroup of G, E(N, G) is the universal N-free G space and X is any finite G-CW complex where N acts freely. We explain how some of the results of Hopkins-Kuhn-Ravenel can be recovered for our results.
Journal of the London Mathematical Society, 1996
Communications in Mathematical Physics, 2008
Алгебра и анализ, 1995
Аннотация: We investigate the notion of exact sequences of Hopf algebras. To two Hopf algebras $ ... more Аннотация: We investigate the notion of exact sequences of Hopf algebras. To two Hopf algebras $ A $ and $ B ,andadataconsistingofanactionof, and a data consisting of an action of ,andadataconsistingofanactionof B $ on $ A ,acocycle,acoactionof, a cocycle, a coaction of ,acocycle,acoactionof A $ on $ B ,andaco−cocycleweassociateashortexactsequenceofHopfalgebras, and a co-cocycle we associate a short exact sequence of Hopf algebras ,andaco−cocycleweassociateashortexactsequenceofHopfalgebras0\ to A\ to C\ to B\ to 0$. We define cleft short exact sequences of Hopf algebras and prove that their isomorphism classes are in a bijective correspondence with the quotient set of datas as above such that the cocycle and the co-cocycle are invertible, modulo a ...
Two-vector spaces are a categorization of the usual notion of vector spaces. An analogue notion, ... more Two-vector spaces are a categorization of the usual notion of vector spaces. An analogue notion, two vector bundles, entered in topology through the work of Bass, Dundas, Rognes and Richter. They provide a rst step into the geometric interpretation of elliptic cohomology. Two vec- tor bundles are dened in terms of cocycles. Graeme Segal suggested that two vector bundles should be related to the moduli space of topological eld theories. The moduli space of closed topological eld theories is described by Frobenius manifolds. We shall show that a massive Frobenius manifold carries a natural geometrically dened two vector bundle of rank one. This bundle encodes the information about the Brane sector in a topological eld theory. We shall describe a generalized connection in the two vector bun- dle and show that this structure describes a solution of the open WDVV equations.
Unknown, 1991
We study the modular properties of a formal power series of elliptic operators that correspond to... more We study the modular properties of a formal power series of elliptic operators that correspond to the S (sup 1)-equivariant index of a hypothetical Dirac operator on loop spaces of a manifold twisted by the action of a group. We also show that this interpretation ...
AIP Conference Proceedings, 2006
We study, for Γ a discrete group of finite virtual cohomological dimension the elliptic cohomolog... more We study, for Γ a discrete group of finite virtual cohomological dimension the elliptic cohomology of the classifying space BΓ.
We present an overview of elliptic cohomology and equivariant elliptic cohomology, emphasizing it... more We present an overview of elliptic cohomology and equivariant elliptic cohomology, emphasizing its relations with some classical results of the cohomology and K-theory of classifying spaces of finite groups. Finally we make some remarks about the relevance of elliptic cohomology for the “Monster moonshine” phenomena.
DESCRIPTION We show that if MMM is a Frobenius manifold of dimension nnn such that TxMT_{x} MTxM is s... more DESCRIPTION We show that if MMM is a Frobenius manifold of dimension nnn such that TxMT_{x} MTxM is semisimple for every xinMx \in MxinM, then there exists a canonical 2-vector bundle mathcalB\mathcal{B}mathcalB over MMM of rank nnn. This 2-vector bundle encodes the information about the maximal category of DDD-branes associated to the open closed topological field theories defined by the Frobenius algebras TxMT_{x} MTxM. In particular this construction answers a conjecture of Graeme Segal in~\cite{segal07:_what_is_ellip_objec}. We also explain the relation of the labels of the DDD-branes to Azumaya algebras and twisted vector bundles on the spectral cover SSS of MMM.
Michigan Mathematical Journal, 1996
Letters in Mathematical Physics, 1994
We define new quantizations of the Heisenberg group by introducing new quantizations in the unive... more We define new quantizations of the Heisenberg group by introducing new quantizations in the universal enveloping algebra of its Lie algebra. Matrix coefficients of the Stone-von Neumann representation are preserved by these new multiplications on the algebra of functions on the Heisenberg group. Some of the new quantizations provide also a new multiplication in the algebra of theta functions; we obtain in this way Sklyanin algebras.
Journal of Pure and Applied Algebra, 1998
Let G be a finite group of order (GI odd and let 6Y~*(-)~?@[l/lGl] denote elliptic cohomology ten... more Let G be a finite group of order (GI odd and let 6Y~*(-)~?@[l/lGl] denote elliptic cohomology tensored by Z[l/lGl]. Then we give a description of &Y*(E(N,G) x ,vX) @ Z[l/lGl], where N is a normal subgroup of G, E(N, G) is the universal N-free G space and X is any finite G-CW complex where N acts freely. We explain how some of the results of Hopkins-Kuhn-Ravenel can be recovered for our results.
Journal of the London Mathematical Society, 1996
Communications in Mathematical Physics, 2008
Алгебра и анализ, 1995
Аннотация: We investigate the notion of exact sequences of Hopf algebras. To two Hopf algebras $ ... more Аннотация: We investigate the notion of exact sequences of Hopf algebras. To two Hopf algebras $ A $ and $ B ,andadataconsistingofanactionof, and a data consisting of an action of ,andadataconsistingofanactionof B $ on $ A ,acocycle,acoactionof, a cocycle, a coaction of ,acocycle,acoactionof A $ on $ B ,andaco−cocycleweassociateashortexactsequenceofHopfalgebras, and a co-cocycle we associate a short exact sequence of Hopf algebras ,andaco−cocycleweassociateashortexactsequenceofHopfalgebras0\ to A\ to C\ to B\ to 0$. We define cleft short exact sequences of Hopf algebras and prove that their isomorphism classes are in a bijective correspondence with the quotient set of datas as above such that the cocycle and the co-cocycle are invertible, modulo a ...
Two-vector spaces are a categorization of the usual notion of vector spaces. An analogue notion, ... more Two-vector spaces are a categorization of the usual notion of vector spaces. An analogue notion, two vector bundles, entered in topology through the work of Bass, Dundas, Rognes and Richter. They provide a rst step into the geometric interpretation of elliptic cohomology. Two vec- tor bundles are dened in terms of cocycles. Graeme Segal suggested that two vector bundles should be related to the moduli space of topological eld theories. The moduli space of closed topological eld theories is described by Frobenius manifolds. We shall show that a massive Frobenius manifold carries a natural geometrically dened two vector bundle of rank one. This bundle encodes the information about the Brane sector in a topological eld theory. We shall describe a generalized connection in the two vector bun- dle and show that this structure describes a solution of the open WDVV equations.