2019, ISBN 9783030172718, 181

eBook

Journal of Algebra, ISSN 0021-8693, 03/2020, Volume 546, pp. 457 - 466

Twisted Lefschetz numbers are extensions of the ordinary Lefschetz numbers for cohomologies with values in flat bundles. As a generalization of linearization...

Topological fixed point theory | Infra-solvmanifold | Cohomology of algebraic group | Twisted Lefschetz number | MATHEMATICS | SUBGROUPS

Topological fixed point theory | Infra-solvmanifold | Cohomology of algebraic group | Twisted Lefschetz number | MATHEMATICS | SUBGROUPS

Journal Article

Advances in Mathematics, ISSN 0001-8708, 07/2019, Volume 351, pp. 195 - 235

We determine the group of reductive cohomological degree 3 invariants of all split semisimple groups of types B, C, and D. We also present a complete...

Unramified cohomology | Galois cohomology | Reductive algebraic group | Classifying space | Cohomological invariants | Torsor | MATHEMATICS | DISCRIMINANT

Unramified cohomology | Galois cohomology | Reductive algebraic group | Classifying space | Cohomological invariants | Torsor | MATHEMATICS | DISCRIMINANT

Journal Article

Advances in Mathematics, ISSN 0001-8708, 07/2019, Volume 351, pp. 495 - 569

We consider a generalization of (pro)algebraic loops defined on general categories of algebras and the dual notion of a coloop bialgebra suitable to represent...

Cogroups | Non-associative algebras | Coloops | Loops | Algebraic groups | Formal diffeomorphisms | Algebra | Group Theory | Mathematics

Cogroups | Non-associative algebras | Coloops | Loops | Algebraic groups | Formal diffeomorphisms | Algebra | Group Theory | Mathematics

Journal Article

85.
Full Text
Complete reducibility of subgroups of reductive algebraic groups over nonperfect fields I

Journal of Algebra, ISSN 0021-8693, 10/2016, Volume 463, pp. 168 - 187

Let k be a nonperfect field of characteristic 2. Let G be a k-split simple algebraic group of type E6 (or G2) defined over k. In this paper, we present the...

Complete reducibility | Separability | Spherical buildings | Algebraic groups | MATHEMATICS | UNIPOTENT | BUILDINGS

Complete reducibility | Separability | Spherical buildings | Algebraic groups | MATHEMATICS | UNIPOTENT | BUILDINGS

Journal Article

Journal of Algebra, ISSN 0021-8693, 01/2014, Volume 397, pp. 666 - 688

Let k be an arbitrary field, let G be a (smooth) linear algebraic group over k, and let U be a vector group over k on which G acts by automorphisms of...

Algebraic groups | Representations and cohomology | MATHEMATICS

Algebraic groups | Representations and cohomology | MATHEMATICS

Journal Article

Journal of Algebra, ISSN 0021-8693, 07/2013, Volume 385, pp. 14 - 26

Let G be a reductive algebraic group over an algebraically closed field k of characteristic p>0, and assume p is good for G. Let P be a parabolic subgroup with...

Algebraic groups | Support varieties for modules | ALGEBRAIC-GROUPS | MATHEMATICS | GROUP SCHEMES | COHOMOLOGY | SUPPORT VARIETIES

Algebraic groups | Support varieties for modules | ALGEBRAIC-GROUPS | MATHEMATICS | GROUP SCHEMES | COHOMOLOGY | SUPPORT VARIETIES

Journal Article

MATHEMATISCHE ZEITSCHRIFT, ISSN 0025-5874, 04/2020, Volume 294, Issue 3-4, pp. 1749 - 1757

Fixing a subgroup Gamma in a group G, the full commensurability growth function assigns to each n the cardinality of the set of subgroups Delta of G with...

MATHEMATICS | LATTICES | Commensurators | Residually Finite groups | Algebraic groups | SUBGROUP GROWTH

MATHEMATICS | LATTICES | Commensurators | Residually Finite groups | Algebraic groups | SUBGROUP GROWTH

Journal Article

Glasnik Matematicki, ISSN 0017-095X, 2016, Volume 51, Issue 2, pp. 335 - 343

We use a p-adic analogue of the analytic subgroup theorem of Wustholz to deduce the transcendence and linear independence of some new classes of p-adic...

Transcendence theory | Commutative algebraic groups | P-adic numbers | p-adic numbers | ALGEBRAIC-GROUPS | MATHEMATICS | GROUP VARIETIES | MATHEMATICS, APPLIED | transcendence theory

Transcendence theory | Commutative algebraic groups | P-adic numbers | p-adic numbers | ALGEBRAIC-GROUPS | MATHEMATICS | GROUP VARIETIES | MATHEMATICS, APPLIED | transcendence theory

Journal Article

Canadian Mathematical Bulletin, ISSN 0008-4395, 12/2016, Volume 59, Issue 4, pp. 824 - 833

We show that the conjectural criterion of p-incompressibility for products of projective homogeneous varieties in terms of the factors, previously known in a...

Chow groups and motives | Projective homogeneous varieties | Algebraic groups | Canonical dimension and incompressibility | ALGEBRAIC-GROUPS | MATHEMATICS | algebraic groups | projective homogeneous varieties | canonical dimension and incompressibility | P-DIMENSION | ESSENTIAL DIMENSION

Chow groups and motives | Projective homogeneous varieties | Algebraic groups | Canonical dimension and incompressibility | ALGEBRAIC-GROUPS | MATHEMATICS | algebraic groups | projective homogeneous varieties | canonical dimension and incompressibility | P-DIMENSION | ESSENTIAL DIMENSION

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 06/2019, Volume 147, Issue 6, pp. 2331 - 2347

Let G be a simple algebraic group over the algebraic closure of \mathbb{F}_p ( p prime), and let G(q) denote a corresponding finite group of Lie-type over...

generation | MATHEMATICS | MATHEMATICS, APPLIED | PROBABILITY | Generation of groups | random generation | algebraic groups | SUBGROUPS | asymptotic group theory

generation | MATHEMATICS | MATHEMATICS, APPLIED | PROBABILITY | Generation of groups | random generation | algebraic groups | SUBGROUPS | asymptotic group theory

Journal Article

Journal of Algebra, ISSN 0021-8693, 06/2017, Volume 480, pp. 423 - 449

We consider first-order linear difference systems over C(x), with respect to a difference operator σ that is either a shift σ:x↦x+1, q-dilation σ:x↦qx with...

Linear differential algebraic groups | Hypertranscendence | Differential Galois theory of difference equations | Differential algebra | Difference algebra | ALGEBRAIC-GROUPS | MATHEMATICS | Algebra | Singers

Linear differential algebraic groups | Hypertranscendence | Differential Galois theory of difference equations | Differential algebra | Difference algebra | ALGEBRAIC-GROUPS | MATHEMATICS | Algebra | Singers

Journal Article

Advances in Mathematics, ISSN 0001-8708, 10/2018, Volume 336, pp. 299 - 315

Let the pair (G,M)R denote a group G acting on an R-module M, R a unitary ring. We ask for the existence of an R-local space X such that (E(X),πk(X))R is...

Rational homotopy theory | Invariant theory | Homotopy equivalences | Linear algebraic groups | MATHEMATICS

Rational homotopy theory | Invariant theory | Homotopy equivalences | Linear algebraic groups | MATHEMATICS

Journal Article

94.
Full Text
Rationality of cycles over function field of exceptional projective homogeneous varieties

Journal of the Ramanujan Mathematical Society, ISSN 0970-1249, 2014, Volume 29, Issue 1, pp. 119 - 132

In this article we prove a result comparing rationality of algebraic cycles over the function field of a projective homogeneous variety under a linear...

ALGEBRAIC-GROUPS | MATHEMATICS | OPERATIONS

ALGEBRAIC-GROUPS | MATHEMATICS | OPERATIONS

Journal Article

2013, CRM monograph series, ISBN 9780821894415, Volume 31, xxvi, 234

Book

Journal of Algebra, ISSN 0021-8693, 06/2017, Volume 480, pp. 385 - 422

Let G be a simple linear algebraic group over an algebraically closed field K of characteristic p≥0 and let V be an irreducible rational G-module with highest...

Representation theory of algebraic groups | Classical groups | Chevalley groups | Quadratic forms | Algebraic groups | SELF-DUAL MODULES | FIELDS | REPRESENTATIONS | MATHEMATICS | QUADRATIC TYPE | SYMMETRIC GROUP | CHARACTERISTIC-2 | BRANCHING-RULES | WEIGHTS | SYMPLECTIC GROUPS | WEYL MODULES | Mathematics - Group Theory

Representation theory of algebraic groups | Classical groups | Chevalley groups | Quadratic forms | Algebraic groups | SELF-DUAL MODULES | FIELDS | REPRESENTATIONS | MATHEMATICS | QUADRATIC TYPE | SYMMETRIC GROUP | CHARACTERISTIC-2 | BRANCHING-RULES | WEIGHTS | SYMPLECTIC GROUPS | WEYL MODULES | Mathematics - Group Theory

Journal Article

Transformation Groups, ISSN 1083-4362, 12/2015, Volume 20, Issue 4, pp. 1141 - 1153

Let G be a simple algebraic group over an algebraically closed field of characteristic p, and assume that p is a separably good prime for G. Let P be a...

ALGEBRAIC-GROUPS | MATHEMATICS | UNIPOTENT ELEMENTS | CENTRALIZERS | SUBGROUPS

ALGEBRAIC-GROUPS | MATHEMATICS | UNIPOTENT ELEMENTS | CENTRALIZERS | SUBGROUPS

Journal Article

Journal of Algebra, ISSN 0021-8693, 05/2019, Volume 526, pp. 188 - 210

In a recent paper, [14], S. Doty and J. M. Douglass consider the degree r component Lr(E) of the free Lie algebra L(E) on an n-dimensional vector space E over...

Centraliser algebra | Lie module | Algebraic group | Tilting module | SCHUR ALGEBRAS | MATHEMATICS | Algebra

Centraliser algebra | Lie module | Algebraic group | Tilting module | SCHUR ALGEBRAS | MATHEMATICS | Algebra

Journal Article

Forum Mathematicum, ISSN 0933-7741, 11/2015, Volume 27, Issue 6, pp. 3461 - 3475

In a previous paper, Broussous and the author prove that for symmetric spaces of the form )/ ), where is a reductive group defined and split over a -adic field...

distinguished representations | 22E50 | Steinberg representation | quadratic characters | 20G25 | adic algebraic groups | p-adic algebraic groups | MATHEMATICS | MATHEMATICS, APPLIED

distinguished representations | 22E50 | Steinberg representation | quadratic characters | 20G25 | adic algebraic groups | p-adic algebraic groups | MATHEMATICS | MATHEMATICS, APPLIED

Journal Article

Mathematische Zeitschrift, ISSN 0025-5874, 2/2018, Volume 288, Issue 1, pp. 361 - 381

This paper is on the inverse parameterized differential Galois problem. We show that surprisingly many groups do not occur as parameterized differential Galois...

34M50 | 14H25 | 12H05 | Linear differential algebraic groups | 34M03 | Mathematics | Patching | Parameterized Picard–Vessiot theory | Galois descent | Inverse differential Galois problem | 34M15 | Mathematics, general | 20G15 | ALGEBRAIC-GROUPS | MATHEMATICS | FIELDS | PICARD-VESSIOT EXTENSIONS | EQUATIONS | Parameterized Picard-Vessiot theory

34M50 | 14H25 | 12H05 | Linear differential algebraic groups | 34M03 | Mathematics | Patching | Parameterized Picard–Vessiot theory | Galois descent | Inverse differential Galois problem | 34M15 | Mathematics, general | 20G15 | ALGEBRAIC-GROUPS | MATHEMATICS | FIELDS | PICARD-VESSIOT EXTENSIONS | EQUATIONS | Parameterized Picard-Vessiot theory

Journal Article

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