Irreducible modules over finite simple Lie pseudoalgebras II. Primitive pseudoalgebras of type K
One of the algebraic structures that has emerged recently in the study of the operator product expansions of chiral fields in conformal field theory is that of a Lie conformal algebra. A Lie pseudoalgebra is a generalization of the notion of a Lie conformal algebra for which C[∂] is replaced by the...
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Elsevier BV
2018
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| Online Access: | http://hdl.handle.net/1721.1/115985 https://orcid.org/0000-0002-2860-7811 |
| _version_ | 1811095833886588928 |
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| author | Bakalov, Bojko D’Andrea, Alessandro Kac, Victor |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Bakalov, Bojko D’Andrea, Alessandro Kac, Victor |
| author_sort | Bakalov, Bojko |
| collection | MIT |
| description | One of the algebraic structures that has emerged recently in the study of the operator product expansions of chiral fields in conformal field theory is that of a Lie conformal algebra. A Lie pseudoalgebra is a generalization of the notion of a Lie conformal algebra for which C[∂] is replaced by the universal enveloping algebra H of a finite-dimensional Lie algebra. The finite (i.e.,finitely generated over H) simple Lie pseudoalgebras were classified in our previous work (Bakalov etal., 2001) [2] . The present paper is the second in our series on representation theory of simple Lie pseudoalgebras. In the first paper we showed that any finite irreducible module over a simple Lie pseudoalgebra of type W or S is either an irreducible tensor module or the kernel of the differential in a member of the pseudo de Rham complex. In the present paper we establish a similar result for Lie pseudoalgebras of type K, with the pseudo de Rham complex replaced by a certain reduction called the contact pseudo de Rham complex. This reduction in the context of contact geometry was discovered by Rumin. |
| first_indexed | 2024-09-23T16:30:05Z |
| format | Article |
| id | mit-1721.1/115985 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2024-09-23T16:30:05Z |
| publishDate | 2018 |
| publisher | Elsevier BV |
| record_format | dspace |
| spelling | mit-1721.1/1159852022-10-02T08:11:49Z Irreducible modules over finite simple Lie pseudoalgebras II. Primitive pseudoalgebras of type K Bakalov, Bojko D’Andrea, Alessandro Kac, Victor Massachusetts Institute of Technology. Department of Mathematics Kac, Victor One of the algebraic structures that has emerged recently in the study of the operator product expansions of chiral fields in conformal field theory is that of a Lie conformal algebra. A Lie pseudoalgebra is a generalization of the notion of a Lie conformal algebra for which C[∂] is replaced by the universal enveloping algebra H of a finite-dimensional Lie algebra. The finite (i.e.,finitely generated over H) simple Lie pseudoalgebras were classified in our previous work (Bakalov etal., 2001) [2] . The present paper is the second in our series on representation theory of simple Lie pseudoalgebras. In the first paper we showed that any finite irreducible module over a simple Lie pseudoalgebra of type W or S is either an irreducible tensor module or the kernel of the differential in a member of the pseudo de Rham complex. In the present paper we establish a similar result for Lie pseudoalgebras of type K, with the pseudo de Rham complex replaced by a certain reduction called the contact pseudo de Rham complex. This reduction in the context of contact geometry was discovered by Rumin. National Science Foundation (U.S.) 2018-05-30T18:11:30Z 2018-05-30T18:11:30Z 2012-10 2010-03 2018-05-23T18:41:07Z Article http://purl.org/eprint/type/JournalArticle 0001-8708 http://hdl.handle.net/1721.1/115985 Bakalov, Bojko, et al. “Irreducible Modules over Finite Simple Lie Pseudoalgebras II. Primitive Pseudoalgebras of Type K.” Advances in Mathematics, vol. 232, no. 1, Jan. 2013, pp. 188–237. https://orcid.org/0000-0002-2860-7811 http://dx.doi.org/10.1016/j.aim.2012.09.012 Advances in Mathematics Creative Commons Attribution-NonCommercial-NoDerivs License http://creativecommons.org/licenses/by-nc-nd/4.0/ application/pdf Elsevier BV arXiv |
| spellingShingle | Bakalov, Bojko D’Andrea, Alessandro Kac, Victor Irreducible modules over finite simple Lie pseudoalgebras II. Primitive pseudoalgebras of type K |
| title | Irreducible modules over finite simple Lie pseudoalgebras II. Primitive pseudoalgebras of type K |
| title_full | Irreducible modules over finite simple Lie pseudoalgebras II. Primitive pseudoalgebras of type K |
| title_fullStr | Irreducible modules over finite simple Lie pseudoalgebras II. Primitive pseudoalgebras of type K |
| title_full_unstemmed | Irreducible modules over finite simple Lie pseudoalgebras II. Primitive pseudoalgebras of type K |
| title_short | Irreducible modules over finite simple Lie pseudoalgebras II. Primitive pseudoalgebras of type K |
| title_sort | irreducible modules over finite simple lie pseudoalgebras ii primitive pseudoalgebras of type k |
| url | http://hdl.handle.net/1721.1/115985 https://orcid.org/0000-0002-2860-7811 |
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