Hochschild and block cohomology varieties are isomorphic

Linckelmann, Markus
April 2010
Journal of the London Mathematical Society;Apr2010, Vol. 81 Issue 2, p389
Academic Journal
We show that the varieties of the Hochschild cohomology of a block algebra and its block cohomology are isomorphic, implying positive answers to questions of Pakianathan and Witherspoon (‘Hochschild cohomology and Linckelmann cohomology for blocks of finite groups’, J. Pure Appl. Algebra 178 (2003) 87–100; ‘Quillen stratification for Hochschild cohomology of blocks’, Trans. Amer. Math. Soc. 358 (2005) 2897–2916). We obtain as a consequence that the cohomology H*(G; k) of a finite group G with coefficients in a field k of characteristic p is a quotient of the Hochschild cohomology of the principal block of kG by a nilpotent ideal.


Related Articles

  • Characterizing Some Small Simple Groups By Their Commuting Involution Graphs. Salarian, M. Reza // Southeast Asian Bulletin of Mathematics;2011, Vol. 35 Issue 3, p467 

    Let G be a finite group isomorphic to A6 or L3(2) and H be a finite group such that the commuting involution graph of G is isomorphic to the commuting involution graph of H. In this paper we show that if H is generated by its involutions, then G ≅H.

  • Finite groups with S-supplemented p-subgroups. Yang, N.; Guo, W.; Shemetkova, O. // Siberian Mathematical Journal;Mar2012, Vol. 53 Issue 2, p371 

    Consider a finite group G. A subgroup is called S-quasinormal whenever it permutes with all Sylow subgroups of G. Denote by B the largest S-quasinormal subgroup of G lying in B. A subgroup B is called S-supplemented in G whenever there is a subgroup T with G = BT and B∩ T ≤ B. A...

  • Approximation properties and linearity of groups. Bryukhanov, O. // Journal of Mathematical Sciences;Jan2013, Vol. 188 Issue 4, p354 

    We present sufficient conditions for an isomorphic representation over a field of a group by matrices. A criterion of the matrix representation for finitely generated groups is given. Bibliography: 7 titles.

  • Recognition by spectrum for simple classical groups in characteristic 2. Vasil'ev, A.; Grechkoseeva, M. // Siberian Mathematical Journal;Nov2015, Vol. 56 Issue 6, p1009 

    A finite group G is said to be recognizable by spectrum if every finite group with the same set of element orders as G is isomorphic to G. We prove that all finite simple symplectic and orthogonal groups over fields of characteristic 2, except S( q), S(2), O (2), and S( q), are recognizable by...

  • Hochschild cohomology for self-injective algebras of tree class D n . I. Volkov, Yu.; Generalov, A. // Journal of Mathematical Sciences;Dec2007, Vol. 147 Issue 5, p7042 

    The minimal projective bimodule resolution is constructed for algebras in a family of self-injective algebras of finite representation type with tree class Dn. Using this resolution, we calculate the dimensions of the Hochschild cohomology groups for the algebras under consideration. The...

  • Representations of a Noncommutative Associative Algebra Related to Quantum Torus of Rank Three. Lin, Shang; Xin, Bin // Acta Mathematica Sinica;Dec2005, Vol. 21 Issue 6, p1521 

    In this paper, we present some modules over the rank–three quantized Weyl algebra, which are closely related to modules over some vertex algebras. The isomorphism classes among these modules are also determined.

  • Quantum Weyl reciprocity for cohomology. Brian J. Parshall; Leonard L. Scott // Proceedings of the London Mathematical Society;May2005, Vol. 90 Issue 3, p655 

    We study the relationship between the cohomology of $q$-Schur algebras and Hecke algebras in type $A$. A key tool, which has independent interest, involves a specific Hecke algebra resolution, introduced in a special case by Deodhar. This resolution is somewhat akin to the Koszul resolution for...

  • On Self-Contragredient Genera Of Z[G]-Lattices. Neiße, Olaf; Weiss, Alfred // Bulletin of the London Mathematical Society;Apr2003, Vol. 35 Issue 2, p203 

    If G is a finite group and V is a finite-dimensional Q[G]-module, V is isomorphic to its contragredient module V*. In general, V need not contain any Z[G]-lattice which is locally isomorphic to its contragredient lattice. Nevertheless, it turns out that for every V there exists another...

  • A reduction theorem for the McKay conjecture. Isaacs, I.M.; Malle, Gunter; Navarro, Gabriel // Inventiones Mathematicae;Aug2007, Vol. 170 Issue 1, p33 

    The McKay conjecture asserts that for every finite group G and every prime p, the number of irreducible characters of G having p�-degree is equal to the number of such characters of the normalizer of a Sylow p-subgroup of G. Although this has been confirmed for large numbers of groups,...


Read the Article


Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics