# On (Co)homology of triangular Banach algebras

• Volume: 67, Issue: 1, page 271-276
• ISSN: 0137-6934

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## Abstract

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Suppose that A and B are unital Banach algebras with units ${1}_{A}$ and ${1}_{B}$, respectively, M is a unital Banach A,B-module, $=\left[\begin{array}{cc}A& M\\ 0& B\end{array}\right]$ is the triangular Banach algebra, X is a unital -bimodule, ${X}_{AA}={1}_{A}X{1}_{A}$, ${X}_{BB}={1}_{B}X{1}_{B}$, ${X}_{AB}={1}_{A}X{1}_{B}$ and ${X}_{BA}={1}_{B}X{1}_{A}$. Applying two nice long exact sequences related to A, B, , X, ${X}_{AA}$, ${X}_{BB}$, ${X}_{AB}$ and ${X}_{BA}$ we establish some results on (co)homology of triangular Banach algebras.

## How to cite

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Mohammad Sal Moslehian. "On (Co)homology of triangular Banach algebras." Banach Center Publications 67.1 (2005): 271-276. <http://eudml.org/doc/282114>.

abstract = {Suppose that A and B are unital Banach algebras with units $1_\{A\}$ and $1_\{B\}$, respectively, M is a unital Banach A,B-module, $= \begin\{bmatrix\} A & M \\ 0 & B\end\{bmatrix\}$ is the triangular Banach algebra, X is a unital -bimodule, $X_\{AA\} = 1_\{A\}X1_\{A\}$, $X_\{BB\} = 1_\{B\}X1_\{B\}$, $X_\{AB\} = 1_\{A\}X1_\{B\}$ and $X_\{BA\} = 1_\{B\}X1_\{A\}$. Applying two nice long exact sequences related to A, B, , X, $X_\{AA\}$, $X_\{BB\}$, $X_\{AB\}$ and $X_\{BA\}$ we establish some results on (co)homology of triangular Banach algebras.},
journal = {Banach Center Publications},
keywords = {triangular Banach algebra; cohomology groups; homology groups; projective module; Ext functor; Tor functor},
language = {eng},
number = {1},
pages = {271-276},
title = {On (Co)homology of triangular Banach algebras},
url = {http://eudml.org/doc/282114},
volume = {67},
year = {2005},
}

TY - JOUR
TI - On (Co)homology of triangular Banach algebras
JO - Banach Center Publications
PY - 2005
VL - 67
IS - 1
SP - 271
EP - 276
AB - Suppose that A and B are unital Banach algebras with units $1_{A}$ and $1_{B}$, respectively, M is a unital Banach A,B-module, $= \begin{bmatrix} A & M \\ 0 & B\end{bmatrix}$ is the triangular Banach algebra, X is a unital -bimodule, $X_{AA} = 1_{A}X1_{A}$, $X_{BB} = 1_{B}X1_{B}$, $X_{AB} = 1_{A}X1_{B}$ and $X_{BA} = 1_{B}X1_{A}$. Applying two nice long exact sequences related to A, B, , X, $X_{AA}$, $X_{BB}$, $X_{AB}$ and $X_{BA}$ we establish some results on (co)homology of triangular Banach algebras.
LA - eng
KW - triangular Banach algebra; cohomology groups; homology groups; projective module; Ext functor; Tor functor
UR - http://eudml.org/doc/282114
ER -

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