Periodic automorphisms of takiff algebras, contractions, and θ-groups
نویسندگان
چکیده
منابع مشابه
Periodic Automorphisms of Takiff Algebras, Contractions, and Θ-groups
Let G be a connected reductive algebraic group with Lie algebra g. The ground field k is algebraically closed and of characteristic zero. Fundamental results in invariant theory of the adjoint representation ofG are primarily associated with C. Chevalley and B. Kostant. Especially, one should distinguish the ”Chevalley restriction theorem” and seminal article of Kostant [5]. Later, Kostant and ...
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Degenerations, contractions and deformations of various algebraic structures play an important role in mathematics and physics. There are many different definitions and special cases of these notions. We try to give a general definition which unifies these notions and shows the connections among them. Here we focus on contractions of Lie algebras and algebraic groups. 1. Contractions, degenerat...
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Suppose that Φ is a reduced irreducible root system, R is an associative commutative ring with unity, G(Φ, R) is the corresponding adjoint Chevalley group, and E(Φ, R) is its elementary subgroup (see Section 5). There are a lot of results (see, e.g., [Wat80], [Pet82], [GMi83], [HO’M89], [Abe93], [Che00], [Bun07], and references therein*) asserting that, under some conditions, all automorphisms ...
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We present solutions to isomorphism problems for various generalized Weyl algebras, including deformations of type-A Kleinian singularities 14] and the algebras similar to U(sl 2) introduced in 31]. For the former, we generalize results of Dixmier 11, 12] on the rst Weyl algebra and the minimal primitive factors of U(sl 2) by nding sets of generators for the group of automorph-isms.
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We show that every automorphism α of a free group Fk of finite rank k has asymptotically periodic dynamics on Fk and its boundary ∂Fk: there exists a positive power α such that every element of the compactum Fk ∪ ∂Fk converges to a fixed point under iteration of α . Further results about the dynamics of α as well as an extension from Fk to word-hyperbolic groups are given in the later sections.
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ژورنال
عنوان ژورنال: Transformation Groups
سال: 2009
ISSN: 1083-4362,1531-586X
DOI: 10.1007/s00031-009-9050-4