摘要
Given a finite dimensional special biserial algebra A with normed basis we obtain the dimension formulae of the first Hochschild homology groups of A and the vector space Alt(DA). As a consequence, an explicit dimension formula of the first Hochschild cohomology group of trivial extension TA = A × DA in terms of the combinatorics of the quiver and relations is determined.
Given a finite dimensional special biserial algebraA with normed basis we obtain the dimension formulae of the first Hochschild homology groups ofA and the vector spaceAlt(DA). As a consequence, an explicit dimension formula of the first Hochschild cohomology group of trivial extensionTA = A ?DA in terms of the combinatorics of the quiver and relations is determined.
基金
This work was supported by the National Natural Science Foundation of China (Grant No. 10201004).
