题目： Mixed Cohomology of Lie Superalgebras
时 间：2019年6月26日 10:30-11:30
Abstract: Supermanifolds are known to admit both differential forms and integral forms, thus any appropriate super analogue of the de Rham theory should take both types of forms into account. However, the cohomology of Lie superalgebras studied so far in the literature involves only differential forms when interpreted as a de Rham theory for Lie supergroups. Thus a new cohomology theory of Lie superalgebras is needed to fully incorporate differential-integral forms, and we investigate such a theory here. This new cohomology is defined by a BRST complex of Lie superalgebra modules, and includes the standard Lie superalgebra cohomology as a special case. General properties expected of a cohomology theory are established for the new cohomology, and examples of the new cohomology groups are computed. This is a joint work with R.B. Zhang.
苏育才，同济大学数学系特聘教授，同济大学数学研究所所长，国家杰出青年基金获得者，主持国家自然科学基金重点项目。主要研究领域为李（超）代数及其表示理论，特别是在李超代数特征标的相关研究上，做出了很多重要成果。现为《Algebra Colloquium》、《Journal of Algebra and Applications》、《数学学报》等多个学术杂志的编委。发表学术论文100多篇。