Cohomology of split algebras and of trivial extensions

被引:16
作者
Cibils, C
Marcos, E
Redondo, MJ
Solotar, A
机构
[1] Univ Montpellier 2, Dept Math, F-34095 Montpellier 5, France
[2] Univ Sao Paulo, Dept Matemat, BR-05315970 Sao Paulo, SP, Brazil
[3] Univ Nacl Sur, Dept Matemat, RA-8000 Bahia Blanca, Argentina
[4] Univ Buenos Aires, Fac Ciencias Exactas & Nat, Dept Matemat, RA-1428 Buenos Aires, DF, Argentina
关键词
D O I
10.1017/S0017089502008959
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We consider associative algebras Lambda over a field provided with a direct sum decomposition of a two-sided ideal M and a sub-algebra A - examples are provided by trivial extensions or triangular type matrix algebras. In this relative and split setting we describe a long exact sequence computing the Hochschild cohomology of Lambda. We study the connecting homomorphism using the cup-product and we infer several results, in particular the first Hochschild cohomology group of a trivial extension never vanishes.
引用
收藏
页码:21 / 40
页数:20
相关论文
共 18 条
[1]  
[Anonymous], 1993, CAN MATH SOC P, V14, P431
[2]   The simple connectedness of a tame tilted algebra [J].
Assem, I ;
Marcos, EN ;
de la Peña, JA .
JOURNAL OF ALGEBRA, 2001, 237 (02) :647-656
[3]  
Assem I., 1997, ALGEBRES MODULES
[4]   Cohomology of morphisms [J].
Bendiffalah, B ;
Guin, D .
COMMUNICATIONS IN ALGEBRA, 1998, 26 (12) :3939-3951
[5]   Artin algebras with loops but no outer derivations [J].
Buchweitz, RO ;
Liu, SP .
ALGEBRAS AND REPRESENTATION THEORY, 2002, 5 (02) :149-162
[6]  
Cartan H., 1956, HOMOLOGICAL ALGEBRA
[7]  
CIBILS C, 2000, LECT NOTES PURE APPL, V210
[8]   ON DEFORMATION OF RINGS + ALGEBRAS [J].
GERSTENHABER, M .
ANNALS OF MATHEMATICS, 1964, 79 (01) :59-&
[9]  
GREEN EL, IN PRESS COMM ALGEBR
[10]  
HAPPEL D, 1990, BANACH CTR PUBL 1, V26, P303