Hochschild cohomology of algebras of quaternion type. III. Algebras with a small parameter

For algebras of quaternion type in the family $Q(2\mathcal B)_1$ which have a “small” natural parameter, we describe the Hochschild cohomology algebra. We use in the corresponding calculation a beforehand constructed 4-periodic bimodule resolution for the algebras under consideration. As result, we complete a description of the Hochschild cohomology algebra for all algebras of quaternion type with 2 simple modules in characteristic two. Bibl. – 7 titles.