2024 Extensions of nilpotent blocks

Extensions of nilpotent blocks

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August undefined, 2024

WebMar 14, 2012 · Download PDF Abstract: The main purpose of this paper is to prove that the extensions of a nilpotent block algebra and its Glauberman correspondent block algebra are Morita equivalent under an additional group-theoretic condition. In particular, Harris and Linckelman's theorem and Koshitani and Michler's theorem are covered. The ingredient …

Block extensions, local categories, and basic Morita equivalences

Webdo not assume here that the block b is nilpotent. Theorem 1.1. Consider the block extension A = bOG and the G¯-graded crossed product Aδ = jAj, where j ∈ δ. Assume that B = bOH is an inertial block. Then the following statements hold. a) The bimodule inducing the Morita equivalence between B and Oα(Q⋊E˜H(Qδ)) is G¯-invariant. WebThe main purpose of this paper is to prove that the extensions of a nilpotent block algebra and its Glauberman correspondent block algebra are Morita equivalent under an additional group‐theoretic condition (see Theorem 1.6); in particular, Harris and Linckelman's theorem and Koshitani and Michler's theorem are covered (see Theorems 7.5 and 7.6). lamb purses handbags

On the Characters of Nilpotent Blocks over Small Ground-Fields

WebOct 1, 2011 · There are normal sub-blocks of nilpotent blocks which are NOT nilpotent or, equivalently, nilpotent extensions of non-nilpotent blocks. In this paper we … WebApr 9, 2010 · There are normal sub-blocks of nilpotent blocks which are NOT nilpotent or, equivalently, nilpotent extensions of non-nilpotent blocks. In this paper we determine the source algebra structure of the non-nilpotent blocks involved in these situations. Actually, we introduce a new type of blocks - called the inertial blocks - which include … WebMay 23, 2010 · Külshammer B., Puig L.: Extensions of nilpotent blocks. Invent. math. 102, 17–71 (1990) Article MathSciNet MATH Google Scholar Puig L.: Pointed groups … lamb raan near me

Extensions of nilpotent blocks SpringerLink

A Frobenius theorem for blocks Semantic Scholar

WebMar 26, 2024 · In this guise it's a generalization of being abelian. An extension of a group G is a group E such that G is a quotient of E. It's actually slightly more--it's a short exact … WebMar 26, 2024 · In this guise it's a generalization of being abelian. An extension of a group G is a group E such that G is a quotient of E. It's actually slightly more--it's a short exact sequence 1 → A → E → G → 1, effectively a "witness" to the fact that G is a quotient of E. A central extension is a group extension as above where additionally A is ... lamb racing strutsWebSep 25, 2024 · Along the way, we give alternative proofs of the results of "B. Kulshammer, L. Puig, {\it Extensions of nilpotent blocks}, Invent. Math., \textbf{102} (1990), 17--71" and "L. Puig, Y. Zhou, {\it Glauberman correspondents and extensions of nilpotent block algebras}, J. London Math. Soc \textbf{85} (2012), 809--837" on extensions of nilpotent ... jerry\\u0027s artarama framing

"WebExtensions of nilpotent blocks. Lluis Puig; Burkhard Külshammer. Inventiones mathematicae (1990) Volume: 102, Issue: 1, page 17-72; ISSN: 0020-9910; 1432 … " - Extensions of nilpotent blocks

Extensions of nilpotent blocks

WebMar 14, 2012 · Download PDF Abstract: The main purpose of this paper is to prove that the extensions of a nilpotent block algebra and its Glauberman correspondent block … WebMar 19, 2012 · The main purpose of this paper is to prove that the extensions of a nilpotent block algebra and its Glauberman correspondent block algebra are Morita equivalent under an additional group-theoretic condition (see Theorem 1.6); in particular, Harris and Linckelman's theorem and Koshitani and Michler's theorem are covered (see …

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Web2) Ever quotient group of a nilpotent group is nilpotent. Proof. Exercise. 24.15 Note. The properties of nilpotent group given in Theorem 24.14 are analogous to the ﬁrst two properties of solvable groups from Theorem 23.6.The third part of that theorem (if H, G/H are solvable then so is G)isnottruefor nilpotent groups. For example, take G = G WebJan 1, 2002 · Nilpotent extensions of blocks. Article. Oct 2011; Lluis Puig; There are normal sub-blocks of nilpotent blocks which are NOT nilpotent or, equivalently, nilpotent extensions of non-nilpotent ...

WebNov 1, 2001 · On blocks with nilpotent coefficient extensions. Algebra Represent. Theory, 1 (1998), pp. 27-73. View in Scopus Google Scholar. 5. I.M. Isaacs. Character Theory of … WebDec 1, 2008 · Glauberman correspondents and extensions of nilpotent block algebras. J. London Math. Soc. (2) 85809–837.[Crossref] [Google Scholar]] which is about the extension of a nilpotent block and its ...

WebMar 19, 2012 · The main purpose of this paper is to prove that the extensions of a nilpotent block algebra and its Glauberman correspondent block algebra are Morita … WebSemantic Scholar extracted view of "Extensions of nilpotent blocks" by B. Külshammer et al.

WebApr 13, 2024 · Extensions of finite-dimensional nilpotent Lie algebras, in particular, solvable extensions, are considered. Some properties of maximal extensions are prov ... =J_2(1)\) is the second-order Jordan block with eigenvalue \(1\). Let us show that this Lie algebra \(L\) is an inclusion-maximal extension of the Abelian Lie algebra \(k^2\).

http://www.math.buffalo.edu/~badzioch/MTH619/Lecture_Notes_files/MTH619_week8.pdf lamb raan masalaWebThe algebraic structure of nilpotent blocks was determined in [10] and then generalized to extensions of nilpotent blocks (see [8]). The main results in [2,8,10] hold over algebraically closed ﬁelds and it is very interesting to generalize them to arbitrary ﬁelds. Fan Yun ﬁrstly deﬁned nilpotent blocks over arbitrary ﬁelds and then gener- jerry\\u0027s artarama gessobordWebthe structure of the nilpotent blocks of A. Let n 1 n 2 n r 1 be the sizes of the nilpotent blocks in the Jordan form of A. In view of the computation of the square of a Jordan block, a necessary and suﬃcient condition for Ato have a square root is that n 2i n 2i 1 lies in f0;1gfor each iwith 2i r, and, if ris odd, n r…1. This is equiv- jerry\u0027s artarama easelsWebadshelp[at]cfa.harvard.edu The ADS is operated by the Smithsonian Astrophysical Observatory under NASA Cooperative Agreement NNX16AC86A jerry\u0027s artarama gessobordWebAbstract. In this paper, with a suitable condition, we describe the algebraic structure of block extensions of nilpotent blocks over arbitrary fields, thus generalize the main result of B ... lamb rack adalahWebMay 1, 2024 · Free extensions of graded Artinian algebras were introduced by T. Harima and J. Watanabe, and were shown to preserve the strong Lefschetz property. The Jordan type of a multiplication map m by a nilpotent element of an Artinian algebra is the partition determining the sizes of the blocks in a Jordan matrix for m. jerry\u0027s artarama foam boardWebMar 14, 2012 · and Puig’s main results on extensions of nilpotent blocks; the pro of of the existence and uniqueness of the ﬁnite grou p L (see [14, Theorem 1.8] a nd Theorem 3.5 below) is dramatically ... jerry\\u0027s artarama greensboro