Some results on the Hochschild cohomology of group algebras

Author:
A. Pourabbas

Journal:
Proc. Amer. Math. Soc. **135** (2007), 2095-2105

MSC (2000):
Primary 43A20; Secondary 46M20

DOI:
https://doi.org/10.1090/S0002-9939-07-08705-9

Published electronically:
February 2, 2007

MathSciNet review:
2299486

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we investigate structure of the second cohomology of a discrete group . First, for a -set we show that an isomorphism of vector spaces from onto exists, where is the set of orbits of . Next we define the notion of pseudoderivation and apply it for the calculation of .

**1.**R. Brooks,*Some remarks on bounded cohomology*, Riemann surfaces and related topics, Ann. of Math. Studies**97**(1981), 53-63. MR**0624804 (83a:57038)****2.**R. I. Grigorchuk,*Some results on bounded cohomology*, London Math. Soc. Lecture Note series.**203**(1995), 111-163. MR**1320279 (96j:20073)****3.**N. Grønbæk,*Some concepts from group cohomology in the Banach algebra context.*Proc. Banach Algebras 97 Conference, Blaubeuren (1998), pp. 205-222. MR**1656607 (2000d:46087)****4.**A. Ya. Helemskii,*The homology of Banach and topological algebras*(Math. and its Applications), 1989. MR**1093462 (92d:46178)****5.**N. V. Ivanov,*Second bounded cohomology group*, J. Soviet Math.**167**(1988), 117-120. MR**0964260 (90a:55015)****6.**B. E. Johnson,*Cohomology in Banach algebras*, Memoirs Amer. Math. Soc.**127**(1972). MR**0374934 (51:11130)****7.**S. Matsumoto and S. Moruta,*Bounded cohomology of certain groups of homeomorphisms*, Proc. Amer. Math. Soc.**94**(1985), 539-544. MR**0787909 (87e:55006)****8.**A. Pourabbas,*Second cohomology group of group algebras with coefficients in iterated duals.*Proc. Amer. Math. Soc.**132**(2004) no. 5, 1403-1410. MR**2053346 (2005b:43003)****9.**T. Soma,*Existence of non-Banach bounded cohomology*, Topology**37**(1998), no. 1, 179-193. MR**1480885 (99e:55010)**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC (2000):
43A20,
46M20

Retrieve articles in all journals with MSC (2000): 43A20, 46M20

Additional Information

**A. Pourabbas**

Affiliation:
Faculty of Mathematics and Computer Science, Amirkabir University of Technology, 424 Hafez Avenue, Tehran 15914, Iran

Email:
arpabbas@aut.ac.ir

DOI:
https://doi.org/10.1090/S0002-9939-07-08705-9

Received by editor(s):
February 23, 2005

Received by editor(s) in revised form:
March 9, 2006

Published electronically:
February 2, 2007

Communicated by:
Joseph A. Ball

Article copyright:
© Copyright 2007
American Mathematical Society