2024 Support varieties for restricted lie algebras

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 … 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 ...

Support varieties of baby Verma modules Journal of Algebra and …

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. … Weband J. Jantzen [JI] concerning the cohomology of restricted Lie algebras are forerun-ners of the results presented here: finite-dimensional restricted Lie algebras are in 1-1 correspondence with infinitesimal group schemes of height < 1. Our main theo-rems (Theorems 5.2 and 6.7 below) when restricted to infinitesimal group schemes morwenna spear bangor

Varieties of elementary Lie algebras

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. 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 … 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 … morwenna white

Varieties for Modules of Finite Dimensional Hopf Algebras

(Open Access) Modular representations of reductive 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]). WebThe 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 … mined over matter crossword clueWebthe 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 … morwenna thistlethwaite

"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) … " - Support varieties for restricted lie algebras

Support varieties for restricted lie algebras

SUPPORT VARIETIES OF NON-RESTRICTED MODULES …

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 … 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 …

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WebSUPPORT VARIETIES OF NON-RESTRICTED MODULES OVER LIE ALGEBRAS OF REDUCTIVE GROUPS Published online by Cambridge University Press: 01 April 1997 … 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.

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. 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.

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 … 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 …

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

WebResearch 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 … morwen pritchard facebookWebSep 29, 2011 · This is true in special cases for e.g. 1) A is a finite dimensional Hopf algebra [16], 2) A is restricted enveloping algebra of restricted Lie superalgebras [1], 3) A is a Frobenius-Lusztig kernel ... morwenn le normand ageWebSep 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. morwenna\u0027s headdress runescapeWebLet 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 . mined ore that contains 45-60% aluminumWebelementary 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. morwenna\\u0027s headdress runescapeWebSupport 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 morwenna vacationsWebThis 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 … mined potash