Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8896183 | Journal of Algebra | 2018 | 39 Pages |
Abstract
To construct an affine supergroup from a Harish-Chandra pair, Gavarini [2] invented a natural method, which first constructs a group functor and then proves that it is representable. We give a simpler and more conceptual presentation of his construction in a generalized situation, using Hopf superalgebras over a superalgebra. As an application of the construction, given a closed super-subgroup of an algebraic supergroup, we describe the normalizer and the centralizer, using Harish-Chandra pairs. We also prove a tensor product decomposition theorem for Hopf superalgebras, and describe explicitly by cocycle deformation, the difference which results from the two choices of dualities found in literature.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Akira Masuoka, Taiki Shibata,