Results 11 to 20 of about 98 (94)

On Azumaya algebras with a finite automorphism group

International Journal of Mathematics and Mathematical Sciences, 2001
Let B be a ring with 1, C the center of B, and G a finite automorphism group of B. It is shown that if B is an Azumaya algebra such that B=⊕∑g∈GJg where Jg={b∈B|bx=g(x)b   for all   x∈B}, then there exist orthogonal central idempotents {fi∈C|i=1,2,…,m ...
George Szeto, Lianyong Xue
doaj   +2 more sources

On the Grothendieck–Serre conjecture for classical groups

Journal of the London Mathematical Society, Volume 106, Issue 4, Page 2884-2926, December 2022., 2022
Abstract We prove some new cases of the Grothendieck–Serre conjecture for classical groups. This is based on a new construction of the Gersten–Witt complex for Witt groups of Azumaya algebras with involution on regular semilocal rings, with explicit second residue maps; the complex is shown to be exact when the ring is of dimension ⩽2$\leqslant 2$ (or ⩽
Eva Bayer‐Fluckiger, Uriya A. First, Raman Parimala   +2 more
wiley   +1 more source

The enumeration of finite rings

Journal of the London Mathematical Society, Volume 106, Issue 4, Page 3240-3262, December 2022., 2022
Abstract Let p$p$ be a fixed prime. We show that the number of isomorphism classes of finite rings of order pn$p^n$ is pα$p^\alpha$, where α=427n3+O(n5/2)$\alpha =\frac{4}{27}n^3+\mathnormal {O}(n^{5/2})$. This result was stated (with a weaker error term) by Kruse and Price in 1969; a problem with their proof was pointed out by Knopfmacher in 1973.
Simon R. Blackburn, K. Robin McLean
wiley   +1 more source

On the structure of double complexes

Journal of the London Mathematical Society, Volume 104, Issue 2, Page 956-988, September 2021., 2021
Abstract We study consequences and applications of the folklore statement that every double complex over a field decomposes into so‐called squares and zigzags. This result makes questions about the associated cohomology groups and spectral sequences easy to understand.
Jonas Stelzig
wiley   +1 more source

Some torsion classes in the Chow ring and cohomology of BPGLn

Journal of the London Mathematical Society, Volume 103, Issue 1, Page 127-160, January 2021., 2021
Abstract In the integral cohomology ring of the classifying space of the projective linear group PGLn (over C), we find a collection of p‐torsion classes yp,k of degree 2(pk+1+1) for any odd prime divisor p of n, and k⩾0. If, in addition, p2∤n, there are p‐torsion classes ρp,k of degree pk+1+1 in the Chow ring of the classifying stack of PGLn, such ...
Xing Gu
wiley   +1 more source

Motives of Azumaya algebras [PDF]

Journal of the Institute of Mathematics of Jussieu, 2010
AbstractWe study the slice filtration for theK-theory of a sheaf of Azumaya algebrasA, and for the motive of a Severi-Brauer variety, the latter in the case of a central simple algebra of prime degree over a field. Using the Beilinson–Lichtenbaum conjecture, we apply our results to show the vanishing ofSK2(A) for a central simple algebraAof square-free
Kahn, Bruno, Levine, Marc
openaire   +2 more sources

On separable abelian extensions of rings

International Journal of Mathematics and Mathematical Sciences, 1982
Let R be a ring with 1, G(=〈ρ1〉×…×〈ρm〉) a finite abelian automorphism group of R of order n where 〈ρi〉 is cyclic of order ni. for some integers n, ni, and m, and C the center of R whose automorphism group induced by G is isomorphic with G.
George Szeto
doaj   +1 more source

On free ring extensions of degree n

International Journal of Mathematics and Mathematical Sciences, 1981
Nagahara and Kishimoto [1] studied free ring extensions B(x) of degree n for some integer n over a ring B with 1, where xn=b, cx=xρ(c) for all c and some b in B(ρ=automophism of  B), and {1,x…,xn−1} is a basis.
George Szeto
doaj   +1 more source

The wonderful compactification for quantum groups

Journal of the London Mathematical Society, Volume 99, Issue 3, Page 778-806, June 2019., 2019
Abstract In this paper, we introduce a quantum version of the wonderful compactification of a group as a certain noncommutative projective scheme. Our approach stems from the fact that the wonderful compactification encodes the asymptotics of matrix coefficients, and from its realization as a GIT quotient of the Vinberg semigroup.
Iordan Ganev
wiley   +1 more source

Subring Depth, Frobenius Extensions, and Towers

International Journal of Mathematics and Mathematical Sciences, Volume 2012, Issue 1, 2012., 2012
The minimum depth d(B, A) of a subring B⊆A introduced in the work of Boltje, Danz and Külshammer (2011) is studied and compared with the tower depth of a Frobenius extension. We show that d(B, A) < ∞ if A is a finite‐dimensional algebra and Be has finite representation type.
Lars Kadison, Tomasz Brzezinski
wiley   +1 more source