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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
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
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
Journal Article
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
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
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
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
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
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
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
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
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
Journal Article
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
Journal Article
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
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
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
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
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
Journal Article
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