演绎 发表于 2025-3-25 04:45:09
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Lie SuperalgebrasThis part is devoted to the generalization of the Laplace-Casimir operator theory to Lie supergroups. In what follows they are called .. The main result is the formula for the radial parts of the Laplace operators under some general assumptions about Lie supergroup. These assumptions are valid in particular for the Lie supergroups .(.) and .(.).Infusion 发表于 2025-3-25 15:02:08
Laplace-Casimir Operators (General Theory)Let {..} be a homogeneous basis of a Lie superalgebra ., .(..) = 0 for 1 ≤ . ≤ . and .(.) . 1 for . + 1 . + .. The enveloping algebra of . is the associative algebra . (.)with generators .. and the relationsPatrimony 发表于 2025-3-25 17:08:35
The Radial Parts of the Laplace Operators on the Lie Supergroups , and ,Let us denote by .., the invariant polynomial on the Lie algebra .(.|.)向下 发表于 2025-3-25 20:42:11
978-90-481-8392-0Springer Science+Business Media Dordrecht 1987Pessary 发表于 2025-3-26 03:19:54
Overview: 978-90-481-8392-0978-94-017-1963-6Deceit 发表于 2025-3-26 05:41:26
Mathematical Physics and Applied Mathematicshttp://image.papertrans.cn/i/image/474241.jpgEmmenagogue 发表于 2025-3-26 10:45:05
Construction of Representations of Lie Supergroups ,(,) and ,(,)a lexicographic ordering. Let us expand G. into the direct sum G. = G. ⊕ G. where G. consists of all the linear combinations of the root vectors corresponding to positive odd roots and G. consists of the ones corresponding to the negative odd roots.勾引 发表于 2025-3-26 14:25:47
https://doi.org/10.1007/978-94-017-1963-6Algebra; dynamics; linear algebra; mechanics; operator嫌恶 发表于 2025-3-26 19:52:09
Supermanifolds in Generalproposed by A. Grothendieck to develop a unified approach to different geometric theories: theory of smooth manifolds, algebraic and analytic geometries, etc. There is a category of ringed spaces corresponding to each of these theories and the theory of supermanifolds fits into the scheme with only