# On Derived Equivalence of Algebras of Semidihedral Type with Two Simple Modules

## Abstract

The Hochschild cohomology groups of degrees not exceeding 3 are computed for algebras of semidihedral type that form the family SD(2B){sub 1} (from the famous K. Erdmann’s classification). In the calculation, the beforehand construction of the initial part of the minimal projective bimodule resolution is used for algebras from the family under discussion. The obtained results imply that the algebras from the families SD(2B){sub 1} and SD(2B){sub 2} with the same parameters in defining relations are not derived equivalent.

- Authors:

- St.Petersburg State University (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 22773941

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Mathematical Sciences

- Additional Journal Information:
- Journal Volume: 232; Journal Issue: 5; Other Information: Copyright (c) 2018 Springer Science+Business Media, LLC, part of Springer Nature; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1072-3374

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICAL METHODS AND COMPUTING; ALGEBRA; GROUP THEORY; RESOLUTION

### Citation Formats

```
Generalov, A. I., E-mail: ageneralov@gmail.com, and Zaikovskii, A. A., E-mail: anat097@mail.ru.
```*On Derived Equivalence of Algebras of Semidihedral Type with Two Simple Modules*. United States: N. p., 2018.
Web. doi:10.1007/S10958-018-3894-X.

```
Generalov, A. I., E-mail: ageneralov@gmail.com, & Zaikovskii, A. A., E-mail: anat097@mail.ru.
```*On Derived Equivalence of Algebras of Semidihedral Type with Two Simple Modules*. United States. doi:10.1007/S10958-018-3894-X.

```
Generalov, A. I., E-mail: ageneralov@gmail.com, and Zaikovskii, A. A., E-mail: anat097@mail.ru. Wed .
"On Derived Equivalence of Algebras of Semidihedral Type with Two Simple Modules". United States. doi:10.1007/S10958-018-3894-X.
```

```
@article{osti_22773941,
```

title = {On Derived Equivalence of Algebras of Semidihedral Type with Two Simple Modules},

author = {Generalov, A. I., E-mail: ageneralov@gmail.com and Zaikovskii, A. A., E-mail: anat097@mail.ru},

abstractNote = {The Hochschild cohomology groups of degrees not exceeding 3 are computed for algebras of semidihedral type that form the family SD(2B){sub 1} (from the famous K. Erdmann’s classification). In the calculation, the beforehand construction of the initial part of the minimal projective bimodule resolution is used for algebras from the family under discussion. The obtained results imply that the algebras from the families SD(2B){sub 1} and SD(2B){sub 2} with the same parameters in defining relations are not derived equivalent.},

doi = {10.1007/S10958-018-3894-X},

journal = {Journal of Mathematical Sciences},

issn = {1072-3374},

number = 5,

volume = 232,

place = {United States},

year = {2018},

month = {8}

}

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