A review of Lie superalgebra cohomology for pseudoforms

IF 0.5 Q3 MATHEMATICS Archivum Mathematicum Pub Date : 2022-01-01 DOI:10.5817/am2022-5-269
C. Cremonini
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引用次数: 0

Abstract

. This note is based on a short talk presented at the “42nd Win-ter School Geometry and Physics” held in Srni, Czech Republic, January 15th–22nd 2022. We review the notion of Lie superalgebra cohomology and extend it to different form complexes, typical of the superalgebraic setting. In particular, we introduce pseudoforms as infinite-dimensional modules related to sub-superalgebras. We then show how to extend the Koszul-Hochschild-Serre spectral sequence for pseudoforms as a computational method to determine the cohomology groups induced by sub-superalgebras. In particular, we show as an example the case of osp (1 | 4) and choose osp (1 | 2) × sp (2) as sub-algebra. We finally comment on some physical applications of such new cohomology classes related to super-branes. The note is a compact version of [10].
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伪形式的李超代数上同调研究综述
. 这篇笔记是基于2022年1月15日至22日在捷克共和国Srni举行的“第42届Win-ter学校几何和物理”上的一个简短演讲。本文回顾了李超代数上同调的概念,并将其推广到不同形式的复形上,这是典型的超代数集合。特别地,我们引入了伪形式作为与次超代数相关的无限维模块。然后,我们展示了如何扩展伪形式的Koszul-Hochschild-Serre谱序列作为一种计算方法来确定由次超代数诱导的上同调群。特别地,我们以osp(1 | 4)为例,选择osp (1 | 2) × sp(2)作为子代数。最后,对这些新上同类在超膜上的一些物理应用作了评述。该笔记是[10]的精简版。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Archivum Mathematicum
Archivum Mathematicum MATHEMATICS-
CiteScore
0.70
自引率
16.70%
发文量
0
审稿时长
35 weeks
期刊介绍: Archivum Mathematicum is a mathematical journal which publishes exclusively scientific mathematical papers. The journal, founded in 1965, is published by the Department of Mathematics and Statistics of the Faculty of Science of Masaryk University. A review of each published paper appears in Mathematical Reviews and also in Zentralblatt für Mathematik. The journal is indexed by Scopus.
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