We show that the generation problem in Thompson's group F is decidable, i.e., there is an algorithm which decides if a finite set of elements of F generates the whole F. The algorithm makes use of the Stallings 2-core of subgroups of F, which can be defined in an analogous way to the Stallings core of subgroups of a finitely generated free group. ......
We develop axiomatics of highest weight categories and quasi-hereditary algebras in order to incorporate two semi-infinite situations which are in Ringel duality with each other; the underlying posets are either upper finite or lower finite. We also consider various more general sorts of stratified categories. In the upper finite cases, we give an ......
Categorifies tensor products of the fundamental representation of quantum sl2 at prime roots of unity, building upon earlier work where a tensor product of two Weyl modules was categorified.
This volume contains the proceedings of the virtual AMS Special Session on Geometric and Algebraic Aspects of Quantum Groups and Related Topics, held from November 20-21, 2021. Noncommutative algebras and noncommutative algebraic geometry have been an active field of research for the past several decades, with many important applications in ......
In this two part work we prove that for every finitely generated subgroup ? < Out(Fn), either ? is virtually abelian or H2 b (?; R) contains a vector space embedding of 1. The method uses actions on hyperbolic spaces. In Part I we focus on the case of infinite lamination subgroups ?-those for which the set of all attracting laminations of all ......
Let p be a prime. In this paper we investigate finite K{2,p}-groups G which have a subgroup H ? G such that K ? H = NG(K) ? Aut(K) for K a simple group of Lie type in characteristic p, and |G : H| is coprime to p. If G is of local characteristic p, then G is called almost of Lie type in characteristic p. Here G is of local characteristic p means ......
This book develops the machinery of homological algebra and its applications to commutative rings and modules. It assumes familiarity with basic commutative algebra, for example, as covered in the author's book, Commutative Algebra. The first part of the book is an elementary but thorough exposition of the concepts of homological algebra, ......
We reinterpret the main conjecture of [10] on the locally analytic Ext1 in a functorial way using (?, ?)-modules (possibly with t-torsion) over the Robba ring, making it more accurate. Then we prove several special or partial cases of this "improved" conjecture, notably for GL3(?p).
