Classification of Harish-Chandra modules over some Lie algebras related to the Virasoro algebra

Dong Liu

Classification of Harish-Chandra modules over some Lie algebras related to the Virasoro algebra

Representation Theory 2015-11-27 v6 Mathematical Physics math.MP Quantum Algebra Rings and Algebras

Authors: Dong Liu

Abstract

In this paper, we provide a uniform method to thoroughly classify all Harish-Chandra modules over some Lie algebras related to the Virasoro algebras. We first classify such modules over the Lie algebra $W(\varrho)[s]$ for $s=0,\frac12$ . With this result and method, we can also do such works for some Lie algebras and superconformal algebras related to the Virasoro algebra, including the several kinds of Schr\"odinger-Virasoro Lie algebras, which are open up to now.

Keywords

Harish-Chandra modules Virasoro algebra Lie algebras superconformal algebras Schrödinger-Virasoro Lie algebras classification

Cite

@article{arxiv.1011.3438,
  title  = {Classification of Harish-Chandra modules over some Lie algebras related to the Virasoro algebra},
  author = {Dong Liu},
  journal= {arXiv preprint arXiv:1011.3438},
  year   = {2015}
}

Comments

Latex, 13 pages, Journal of Algebra 2015, In Press. arXiv admin note: text overlap with arXiv:math/0510194 by other authors

Classification of Harish-Chandra modules over some Lie algebras related to the Virasoro algebra

Abstract

Keywords

Cite

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