Support varieties for restricted lie algebras
WebSUPPORT VARIETIES OF LIE SUPERALGEBRAS 3 u(osp(1 2)) are tame. Inspired by the similarity between sl2 and osp(1 2) and for further understanding of the representations … WebSUPPORT VARIETIES OF NON-RESTRICTED MODULES OVER LIE ALGEBRAS OF REDUCTIVE GROUPS Published online by Cambridge University Press: 01 April 1997 …
Support varieties for restricted lie algebras
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Websupport varieties of non-restricted modules over lie algebras of reductive groups - volume 55 issue 2 Skip to main content Accessibility help We use cookies to distinguish you from other users and to provide you with a better experience on our websites. WebNov 18, 2003 · Support varieties for any finite dimensional algebra over a field were introduced by Snashall-Solberg using graded subalgebras of the Hochschild cohomology. …
WebLie algebras and their restricted modules (e.g., [12]). Work of Friedlander-Parshall [12] and J. Jantzen [14] provided a description of the cohomological support variety of a restricted g … Webelementary subalgebras of dimension r of a (p-restricted) Lie algebra g for various r ≥ 1. These varieties E(r,g) are the natural ambient varieties for generalized support varieties for restricted representations of g. We identify these varieties in special cases, revealing their interesting and varied geometric structures.
Webof the results presented here: nite dimensional restricted Lie algebras are in 1-1 correspondence with in nitesimal group schemes of height 1. Our main theorems (Theorems 5.2 and 6.7 below) when restricted to in nitesimal group schemes of height 1 signi cantly strengthen previously known cohomological information for restricted Lie algebras. WebIn this paper, we study the restricted cohomology of Lie algebras of semisimple and simply connected algebraic groups in positive characteristics with coefficients in simple restricted modules and their applications in studying the connections between these cohomology with the corresponding ordinary cohomology and cohomology of algebraic groups.
WebSupport varieties for restricted lie algebras E. Friedlander, B. Parshall Published 1 October 1986 Mathematics Inventiones mathematicae View on Springer Save to Library Create Alert Cite 161 Citations Citation Type More Filters A survey of support theories for Lie superalgebras and finite supergroup schemes C. Drupieski, J. Kujawa Mathematics 2024
WebRESTRICTED COHOMOLOGY AND REPRESENTATION THEORY 5 is a restricted Lie algebra. In particular, gln(F) := Matn(F)− is an n2-dimensional restricted Lie algebra for any positive integer n.The so-called Lie algebras of classical type are p-subalgebras of gln(F) for some positive integer n satisfying certain conditions, e.g. sln(F):= {x ∈ gln(F) tr(x)=0} is a … coogee surf camWebA conjecture describing the support variety of Z χ ( λ) via that of its restricted counterpart is given: 𝒱 𝔤 ( Z χ ( λ)) = 𝒱 𝔤 ( Z 0 ( λ)) ∩ 𝔷 𝔤 ( χ). Under the assumption of p ≥ h (the Coxeter number) and λ p -regular, this conjecture is proved when χ falls in the regular nilpotent orbit for any 𝔤 … family all inclusive resorts ozarksWebIn case the characteristic of k is a prime p, and g is a restricted Lie algebra, its restricted enveloping algebra u(g) is a nite dimensional cocommutative Hopf algebra with analogous comultiplication, counit, and antipode. Example 2.4. A= U q(g) or A= u q(g), the in nite dimensional quantum envelop-ing algebras and some nite dimensional ... coogee surf club sydneyWebin a particular class of Lie algebras, called restricted (or Lie p-algebras). This was introduced by Jacobson [19]. The reader is referred to [31, Chapter II] for basic facts on restricted Lie algebras. De nition 1.2.1. A Lie algebra g over kis said to be restricted if there exists a map, [p] : g !g satisfying: 1.ad(x[p]) = ad(x)p for all x2g, 2. coogee swimming lessonsWebMay 18, 2024 · Abstract: This paper investigates cohomology and support varieties for Lie superalgebras and restricted Lie superalgebras over a field of characteristic 2. The … family all inclusive resorts mexicoWebResearch partially supported by the N.S.F. The first author gratefully acknowledges the support of the Institute for Advanced Study Rights and permissions Reprints and Permissions About this article Cite this article Friedlander, E.M., Parshall, B.J. Support … family all-inclusive resorts spainWebelementary subalgebras of dimension r of a (p-restricted) Lie algebra g for various r 1. These varieties E(r;g) are the natural ambient varieties for generalized support varieties for restricted representations of g. We identify these varieties in special cases, revealing their interesting and varied geometric structures. family all inclusives