Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userHomology of general linear groups over infinite fields
171
0
0.0
(
0
)
Authors
Behrooz Mirzaii
Ask ChatGPT about the research
No Arabic abstract
For an infinite field $F$, we study the cokernel of the map of homology groups $H_{n+1}(mathrm{GL}_{n-1}(F),mathbb{k}) to H_{n+1}(mathrm{GL}_{n}(F),mathbb{k})$, where $mathbb{k}$ is a field such that $(n-2)!in mathbb{k}^times$, and the kernel of the natural map $H_{n}big(mathrm{GL}_{n-1}(F),mathbb{Z}big[frac{1}{(n-2)!} big] big) to H_{n}big(mathrm{GL}_{n}(F),mathbb{Z}big[frac{1}{(n-2)!} big]big)$. We give conjectural estimates of these cokernel and kernel and prove our conjectures for $nleq 4$.
rate research
Read More
For a commutative ring R with many units, we describe the kernel of H_3(inc): H_3(GL_2(R), Z) --> H_3(GL_3(R), Z). Moreover we show that the elements of this kernel are of order at most two. As an application we study the indecomposable part of K_3(R).
We study multiplicities of unipotent characters in tensor products of unipotent characters of GL(n,q). We prove that these multiplicities are polynomials in q with non-negative integer coefficients. We study the degree of these polynomials and give a necessary and sufficient condition in terms of the representation theory of symmetric groups for these polynomials to be non-zero.
We survey recent progress in computing with finitely generated linear groups over infinite fields, describing the mathematical background of a methodology applied to design practical algorithms for these groups. Implementations of the algorithms have been used to perform extensive computer experiments.
In this article we study the homology of nilpotent groups. In particular a certain vanishing result for the homology and cohomology of nilpotent groups is proved.
We study five different types of the homology of a Lie algebra over a commutative ring which are naturally isomorphic over fields. We show that they are not isomorphic over commutative rings, even over $mathbb Z,$ and study connections between them. In particular, we show that they are naturally isomorphic in the case of a Lie algebra which is flat as a module. As an auxiliary result we prove that the Koszul complex of a module $M$ over a principal ideal domain that connects the exterior and the symmetric powers $0to Lambda^n Mto M otimes Lambda^{n-1} M to dots to S^{n-1}M otimes M to S^nMto 0 $ is purely acyclic.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
