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pro vyhledávání: '"Benson, David A"'
Autor:
Benson, David J.
The nilCoxeter algebra $\mathcal{N}S_n$ of the symmetric group $S_n$ is the algebra over $\mathbb{Z}$ with generators $Y_i$ ($1\leqslant i\leqslant n-1$), satisfying the braid relations $Y_iY_{i+1}Y_i=Y_{i+1}Y_iY_{i+1}$, $Y_iY_j=Y_jY_i$ ($|j-i|\geqsl
Externí odkaz:
http://arxiv.org/abs/2407.21175
Autor:
Benson, David J., Lim, Kay Jin
Algebras defined over fields of characteristic zero and positive characteristic usually do not behave the same way. However, for certain algebras, for example the group algebras, they behave the same way as the characteristic zero case at good enough
Externí odkaz:
http://arxiv.org/abs/2407.05531
Autor:
Benson, David J., Carlson, Jon F.
Let $G$ be a finite group and $\mathsf{k}$ a field of characteristic $p$. It is conjectured in a paper of the first author and John Greenlees that the thick subcategory of the stable module category StMod$(\mathsf{k}G)$ consisting of modules whose co
Externí odkaz:
http://arxiv.org/abs/2308.09579
Autor:
Benson, David J.
We are given a finite group $H$, an automorphism $\tau$ of $H$ of order $r$, a Galois extension $L/K$ of fields of characteristic zero with cyclic Galois group $\langle\sigma\rangle$ of order $r$, and an absolutely irreducible representation $\rho\co
Externí odkaz:
http://arxiv.org/abs/2306.06280
Autor:
Benson, David J., Greenlees, John
Let $G$ be a finite group and $k$ a field of characteristic $p$. We conjecture that if $M$ is a $kG$-module with $H^*(G,M)$ finitely generated as a module over $H^*(G,k)$ then as an element of the stable module category $\mathsf{StMod}(kG)$, $M$ is c
Externí odkaz:
http://arxiv.org/abs/2305.08580
Autor:
Benson, David J.
Let $G$ be a finite $p$-group, and $\alpha$ an automorphism of the group algebra ${\mathbb F}_pG$. Then $\alpha$ fixes the socle of ${\mathbb F}_pG$ pointwise. More generally, if $k$ is a field of characteristic $p$, and $\alpha$ is a $k$-algebra aut
Externí odkaz:
http://arxiv.org/abs/2303.09940
We relate the generating functions of the dimensions of the Hochschild cohomology in any fixed degree of the symmetric groups with those of blocks of the symmetric groups. We show that the first Hochschild cohomology of a positive defect block of a s
Externí odkaz:
http://arxiv.org/abs/2301.03185
Autor:
Benson, David J.
Thanks to the work of Karin Erdmann, we know a great deal about the representation theory of blocks of finite groups with tame representation type. Our purpose here is to examine the $p$-completed classifying spaces of these blocks and their loop spa
Externí odkaz:
http://arxiv.org/abs/2208.07913
Autor:
Benson, David J.
We answer in the negative a question of Hartley about representations of finite groups, by constructing examples of finite simple groups with arbitrarily large representations whose endomorphism ring consists of just the scalars. We show as a consequ
Externí odkaz:
http://arxiv.org/abs/2208.03787
Autor:
Benson, David, Greenlees, John
Let $G$ be a compact Lie group with maximal torus $T$. If $|N_G(T)/T|$ is invertible in the field $k$ then the algebra of cochains $C^*(BG;k)$ is formal as an $A_\infty$ algebra, or equivalently as a DG algebra.
Comment: 8 pages
Comment: 8 pages
Externí odkaz:
http://arxiv.org/abs/2205.02080