S. Sinelshchikov - Academia.edu (original) (raw)

Uploads

Papers by S. Sinelshchikov

Research paper thumbnail of Quantum enveloping algebras, von Neumann regularity and the Pierce decomposition

This work introduces quantum bialgebras, which differ from the standard U q (sl 2 ) by presence o... more This work introduces quantum bialgebras, which differ from the standard U q (sl 2 ) by presence of von Neumann regular Cartan-like generators and the associated idempotents. Both invertible and von Neumann regular antipodes on such bialgebras are presented explicitly; the latter case leads to a von Neumann-Hopf algebra structure. Also, explicit forms of some particular R-matrices (also invertible and von Neumann regular) are presented, and the latter respects the Pierce

Research paper thumbnail of Classification of U_q (sl_2)-module algebra structures on the quantum plane

We produce a complete list of Uq(sl2)-module algebra structures on the quantum plane. The (uncoun... more We produce a complete list of Uq(sl2)-module algebra structures on the quantum plane. The (uncountable family of) isomorphism classes of such structures are described. The composition series of representations in question are presented. The classical limits of the Uq(sl2)-module algebra structures are discussed.

Research paper thumbnail of Non-compact quantum groups and quantum Harish-Chandra modules

Nuclear Physics B - Proceedings Supplements, 2001

An important problem of the quantum group theory is to construct and classify the Harish-Chandra ... more An important problem of the quantum group theory is to construct and classify the Harish-Chandra modules; it is discussed in this work. The way of producing the principal non-degenerate series representations of the quantum group SUn,n is sketched. A q-analogue for the Penrose transform is described.

Research paper thumbnail of Classification and Structure of Cocycles of Amenable Ergodic Equivalence Relations

Journal of Functional Analysis, 1994

Research paper thumbnail of Locally compact groups appearing as ranges of cocycles of ergodic -actions

Ergodic Theory and Dynamical Systems, 1985

The paper contains the proof of the fact that every solvable locally compact separable group is t... more The paper contains the proof of the fact that every solvable locally compact separable group is the range of a cocycle of an ergodic automorphism. The proof is based on the theory of representations of canonical anticommutation relations and the orbit theory of dynamical systems. The slight generalization of reasoning shows further that this result holds for amenable Lie groups as well and can be also extended to almost connected amenable locally compact separable groups.

Research paper thumbnail of Automorphisms of ergodic groupoids and semidirect products

Journal of Soviet Mathematics, 1990

Research paper thumbnail of Quantum enveloping algebras, von Neumann regularity and the Pierce decomposition

This work introduces quantum bialgebras, which differ from the standard U q (sl 2 ) by presence o... more This work introduces quantum bialgebras, which differ from the standard U q (sl 2 ) by presence of von Neumann regular Cartan-like generators and the associated idempotents. Both invertible and von Neumann regular antipodes on such bialgebras are presented explicitly; the latter case leads to a von Neumann-Hopf algebra structure. Also, explicit forms of some particular R-matrices (also invertible and von Neumann regular) are presented, and the latter respects the Pierce

Research paper thumbnail of Classification of U_q (sl_2)-module algebra structures on the quantum plane

We produce a complete list of Uq(sl2)-module algebra structures on the quantum plane. The (uncoun... more We produce a complete list of Uq(sl2)-module algebra structures on the quantum plane. The (uncountable family of) isomorphism classes of such structures are described. The composition series of representations in question are presented. The classical limits of the Uq(sl2)-module algebra structures are discussed.

Research paper thumbnail of Non-compact quantum groups and quantum Harish-Chandra modules

Nuclear Physics B - Proceedings Supplements, 2001

An important problem of the quantum group theory is to construct and classify the Harish-Chandra ... more An important problem of the quantum group theory is to construct and classify the Harish-Chandra modules; it is discussed in this work. The way of producing the principal non-degenerate series representations of the quantum group SUn,n is sketched. A q-analogue for the Penrose transform is described.

Research paper thumbnail of Classification and Structure of Cocycles of Amenable Ergodic Equivalence Relations

Journal of Functional Analysis, 1994

Research paper thumbnail of Locally compact groups appearing as ranges of cocycles of ergodic -actions

Ergodic Theory and Dynamical Systems, 1985

The paper contains the proof of the fact that every solvable locally compact separable group is t... more The paper contains the proof of the fact that every solvable locally compact separable group is the range of a cocycle of an ergodic automorphism. The proof is based on the theory of representations of canonical anticommutation relations and the orbit theory of dynamical systems. The slight generalization of reasoning shows further that this result holds for amenable Lie groups as well and can be also extended to almost connected amenable locally compact separable groups.

Research paper thumbnail of Automorphisms of ergodic groupoids and semidirect products

Journal of Soviet Mathematics, 1990

Log In