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The first cohomology group of trivial extensions of special biserial algebras |
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| Authors: | |
| Institution: | Department of Mathematics & Computer Sciences, Hubei University, Wuhan 430062, China;Institute of Mathematics, Chinese Academy of Sciences, Beijing 100080, China |
| Abstract: | 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. |
| Keywords: | Hochschild (co)homology trivial extension special biserial algebra |
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