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- Title
Centers of centralizers of nilpotent elements in Lie superalgebras (m|n) or (m|2n).
- Authors
Han, Leyu
- Abstract
Let Ḡ be the simple algebraic supergroup SL (m | n) or (m | 2 n) over ℂ. Let = Lie (Ḡ) = 0 ̄ ⊕ 1 ̄ and let G = Ḡ (ℂ) , where ℂ is considered as a superalgebra concentrated in even degree. Suppose e ∈ 0 ̄ is nilpotent. We describe the centralizer e of e in and its center ( e). In particular, we give bases for e , ( e) and (( e)) G e . We also determine the labeled Dynkin diagram Δ with respect to e and subsequently describe the relation between (( e)) G e and Δ.
- Subjects
DYNKIN diagrams; LIE superalgebras
- Publication
Journal of Algebra & Its Applications, 2022, Vol 21, Issue 1, p1
- ISSN
0219-4988
- Publication type
Article
- DOI
10.1142/S0219498822500062