Support varieties for restricted lie algebras

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August undefined, 2024

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. WebSupport varieties for restricted Lie algebras 555 Proof. We have H*(G,, M)~H*(G, M ")) by [4; 4.4] ~-H*(B, M m) by [11; Theorem 2]. The asserted spectral sequence is the Lyndon …

SUPPORT VARIETIES OF NON-RESTRICTED MODULES …

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. WebOct 5, 2024 · Here, we will present the support variety theory of Erdmann, Holloway, Snashall, Solberg, and Taillefer [21, 50] for self-injective algebras (based on Hochschild cohomology), as well as the closely related generalization to Hopf algebras of support varieties for finite group representations (see, e.g., [25, 27, 29, 40]). twin headed fire dragon

Varieties for Modules of Finite Dimensional Hopf Algebras

WebMay 1, 2024 · We study the spectrum of the cohomology rings of cocommutative Hopf superalgebras, restricted and non-restricted Lie superalgebras, and finite supergroup … 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 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. … tainiomania if only

SUPPORT VARIETIES AND REPRESENTATIONS OF …

Support varieties for restricted lie algebras Semantic Scholar

WebLet g and ! be the Lie algebras of G and K, and let g—ϊ+ί> be the Cartan decomposition of g corres- ponding to ϊ. For any subspace tn of g, we denote by mc the complexification of m. Since G has a faithful matrix representation, we can regard G as a sub- group of a connected Lie group Gc with Lie algebra g c . 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. twin-headed thunder dragonWebMay 18, 2024 · Abstract: This paper investigates cohomology and support varieties for Lie superalgebras and restricted Lie superalgebras over a field of characteristic 2. The … twin headed thunder dragon forbidden memories

"Webin 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. " - Support varieties for restricted lie algebras

Support varieties for restricted lie algebras

WebSupport varieties, Lie superalgebras, ﬁnite supergroup schemes. The ﬁrst author was supported in part by Simons Collaboration Grant for Mathematicians No. 4269055. The second author was supported in part by Simons Collaboration Grant … WebJul 15, 2012 · It is known that support varieties can be defined once the finite generation of cohomology is established, which is hard to prove in general. In this paper, we prove this …

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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 … WebIn 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 ...

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. WebA 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 …

WebApr 1, 1998 · Inspired by these successes, similar theories of support have been developed and successfully applied for different kinds of algebras. For example, for restricted Lie algebras [23], finite ... WebThis paper deals with representations of Lie algebras of reductive groups in prime charateristic. Several results previously known only for restricted representations (on graded structures, filtrations, translation functors) are extended to representations with a non-zero p -character. In a special case in type B 2 all simple modules with a certain p -character are …

WebMay 19, 2024 · intersection of topics that are well-understood (support varieties for restricted Lie algebras) and topics that are not (support varieties for graded objects). 1.2. Main Results. We begin in Section 2 by recalling the deﬁnition of a Lie superalgebra over a ﬁeld of arbitrary characteristic.

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 … twin headed guardian persona 5 royalWebSep 1, 2002 · Support varieties of non-restricted modules over Lie algebras of reductive groups. J. London Math. Soc., 55 (1997), pp. 236-250. View Record in Scopus Google Scholar. 37. A.A. Premet. Complexity of Lie algebra representations and nilpotent elements of the stabilizers of linear forms. Math. Z., 228 (1998), pp. 255-282. twin headed thunder dragon deck tainiomania knowingWebLie 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 … twin headed snakeWebA 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) … twin-head magic wand massagerWebThe main purpose of this paper is to present a common framework where most of the existing occurrences of support varieties fit in. Examples of such are support varieties for finite dimensional algebras, finite groups, restricted finite dimensional Lie algebras, smooth algebraic groups, finite group schemes, stable homotopy categories and complete … twin headed thunder dragon cardWebthe representation theory of restricted Lie algebras. Through their work and the work of those who followed, support varieties for restricted Lie algebras are comparatively well … tainiomania im not a robot