Overgroups of classical groups in linear group over Banach algebras

You, Hong

doi:10.1016/j.jalgebra.2006.03.024

Cited by 6 publications

(3 citation statements)

References 12 publications

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“…But in the case n m 3, by a direct calculation we can see that orthogonal or symplectic group is not contained in the corresponding stabilizer group. 7 This multiplier λ(g) is a one-dimensional representation of the group GLn(R), and thus, λ(g) is a power of the determinant λ = det ⊗l : g → det l (g). From the last, it follows that this multiplier equals 1 for SLn-form of the group.…”

Section: 6mentioning

confidence: 99%

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Overgroups of exterior powers of an elementary group. I. Levels and normalizers

Lubkov¹,

Nekrasov²

2018

Preprint

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In the present paper, we prove the first part in the standard description of groups H lying between m E(n, R) and GL ( n m ) (R). We study the structure of the group m E(n, R) and its relative analogIn the considering case n 3m, the description is explained by the classical notion of level : for every such H we find unique ideal A of the ring R.Motivated by the problem, we prove the coincidence of the following groups: normalizer of m E(n, R), normalizer of m SLn(R), transporter of m E(n, R) into m SLn(R), and a group m GLn(R). This result mainly follows from the found explicit equations for the algebraic group scheme m GLn( ).

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Section: 6mentioning

confidence: 99%

“…• for symplectic, orthogonal, and unitary groups by Nikolai Vavilov and Victor Petrov in [1,2,3,4] and by You Hong, Xing Tao Wang and Cheng Shao Hong in [5,6,7,8];…”

Section: Introductionmentioning

confidence: 99%

Overgroups of exterior powers of an elementary group. I. Levels and normalizers

Lubkov¹,

Nekrasov²

2018

Preprint

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“…Petrov in [9] investigated the overgroups of unitary groups (with hyperbolic form) under a local stable rank condition with form parameter. You in [18,19] classified overgroups of classical groups in linear group over Banach algebras and over commutative rings respectively.…”

Section: Introductionmentioning

confidence: 99%

Overgroups of the elementary unitary group in linear group over commutative rings

Wang¹,

Hong²

2008

Journal of Algebra

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Relative commutator calculus in Chevalley groups

2013

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We revisit localisation and patching method in the setting of Chevalley groups. Introducing certain subgroups of relative elementary Chevalley groups, we develop relative versions of the conjugation calculus and the commutator calculus in Chevalley groups G(Φ, R), rk(Φ) ≥ 2, which are both more general, and substantially easier than the ones available in the literature. For classical groups such relative commutator calculus has been recently developed by the authors in [34,33]. As an application we prove the mixed commutator formula,for two ideals a, b R. This answers a problem posed in a paper by Alexei Stepanov and the second author. O Life, you put thousand traps in my wayDare to try, is what you clearly say Omar Khayam IntroductionOne of the most powerful ideas in the study of groups of points of reductive groups over rings is localisation. It allows to reduce many important problems over arbitrary commutative rings, to similar problems for semi-local rings. Localisation comes in a number of versions. The two most familiar ones are localisation and patching, proposed by Daniel Quillen [55] and Andrei Suslin [65], and localisationcompletion, proposed by Anthony Bak [8].Originally, the above papers addressed the case of the general linear group GL(n, R). Soon thereafter, Suslin himself, Vyacheslav Kopeiko, Marat Tulenbaev, Giovanni Taddei, Leonid Vaserstein, Li Fuan, Eiichi Abe, You Hong, and others proposed workingThe work of the second author was supported by RFFI projects

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Overgroups of classical groups in linear group over Banach algebras

Abstract: All overgroups of elementary unitary groups in linear group GL 2n over Banach algebras with 1 have been described.

Cited by 6 publications

References 12 publications

Overgroups of exterior powers of an elementary group. I. Levels and normalizers

Overgroups of exterior powers of an elementary group. I. Levels and normalizers

Overgroups of the elementary unitary group in linear group over commutative rings

Relative commutator calculus in Chevalley groups

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