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Article: DIRAC COHOMOLOGY FOR DEGENERATE AFFINE HECKE-CLIFFORD ALGEBRAS
Title | DIRAC COHOMOLOGY FOR DEGENERATE AFFINE HECKE-CLIFFORD ALGEBRAS |
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Authors | |
Issue Date | 2017 |
Citation | Transformation Groups, 2017, v. 22, n. 1, p. 125-162 How to Cite? |
Abstract | In this paper, we study the Dirac cohomology theory on a class of algebraic structures. The main examples of this algebraic structure are the degenerate affine Hecke-Clifford algebra of type An-1 by Nazarov and of classical types by Khongsap-Wang. The algebraic structure contains a remarkable subalgebra, which usually refers to Sergeev algebra for type An-1. We define an analogue of the Dirac operator for those algebraic structures. A main result is to relate the central characters of modules of those algebras with the central characters of modules of the Sergeev algebra via the Dirac cohomology. The action of the Dirac operator on certain modules is also computed. Results in this paper could be viewed as a projective version of the Dirac cohomology of the degenerate affine Hecke algebra. |
Persistent Identifier | http://hdl.handle.net/10722/327096 |
ISSN | 2023 Impact Factor: 0.4 2023 SCImago Journal Rankings: 0.844 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Chan, Kei Yuen | - |
dc.date.accessioned | 2023-03-31T05:28:46Z | - |
dc.date.available | 2023-03-31T05:28:46Z | - |
dc.date.issued | 2017 | - |
dc.identifier.citation | Transformation Groups, 2017, v. 22, n. 1, p. 125-162 | - |
dc.identifier.issn | 1083-4362 | - |
dc.identifier.uri | http://hdl.handle.net/10722/327096 | - |
dc.description.abstract | In this paper, we study the Dirac cohomology theory on a class of algebraic structures. The main examples of this algebraic structure are the degenerate affine Hecke-Clifford algebra of type An-1 by Nazarov and of classical types by Khongsap-Wang. The algebraic structure contains a remarkable subalgebra, which usually refers to Sergeev algebra for type An-1. We define an analogue of the Dirac operator for those algebraic structures. A main result is to relate the central characters of modules of those algebras with the central characters of modules of the Sergeev algebra via the Dirac cohomology. The action of the Dirac operator on certain modules is also computed. Results in this paper could be viewed as a projective version of the Dirac cohomology of the degenerate affine Hecke algebra. | - |
dc.language | eng | - |
dc.relation.ispartof | Transformation Groups | - |
dc.rights | This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. | - |
dc.title | DIRAC COHOMOLOGY FOR DEGENERATE AFFINE HECKE-CLIFFORD ALGEBRAS | - |
dc.type | Article | - |
dc.description.nature | published_or_final_version | - |
dc.identifier.doi | 10.1007/s00031-016-9390-9 | - |
dc.identifier.scopus | eid_2-s2.0-84969141490 | - |
dc.identifier.volume | 22 | - |
dc.identifier.issue | 1 | - |
dc.identifier.spage | 125 | - |
dc.identifier.epage | 162 | - |
dc.identifier.eissn | 1531-586X | - |
dc.identifier.isi | WOS:000406751400005 | - |