Journal of Algebra, ISSN 0021-8693, 05/2019

Journal Article

Advances in Mathematics, ISSN 0001-8708, 2010, Volume 225, Issue 3, pp. 1499 - 1522

We determine the universal deformation rings R ( G , V ) of certain mod 2 representations V of a finite group G which belong to a 2-modular block of G whose...

Dihedral defect groups | Universal deformation rings | Quaternion defect groups | MATHEMATICS | NEED | ENDO-TRIVIAL MODULES | BLOCKS | CLASSIFICATION | COMPLETE-INTERSECTIONS | Mathematics - Group Theory

Dihedral defect groups | Universal deformation rings | Quaternion defect groups | MATHEMATICS | NEED | ENDO-TRIVIAL MODULES | BLOCKS | CLASSIFICATION | COMPLETE-INTERSECTIONS | Mathematics - Group Theory

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 2014, Volume 366, Issue 12, pp. 6507 - 6540

Journal Article

Mathematische Zeitschrift, ISSN 0025-5874, 07/2004, Volume 247, Issue 3, pp. 461 - 486

We show that each block whose defect groups intersect pairwise trivially either has cyclic or generalised quaternion defect groups, or is Morita equivalent to...

Mathematics | MATHEMATICS | CLASSICAL-GROUPS | MODULES | 2-BLOCKS | FINITE-GROUPS | QUATERNION | P-LOCAL RANK | CONJECTURE

Mathematics | MATHEMATICS | CLASSICAL-GROUPS | MODULES | 2-BLOCKS | FINITE-GROUPS | QUATERNION | P-LOCAL RANK | CONJECTURE

Journal Article

Journal of Algebra, ISSN 0021-8693, 07/2018, Volume 505, pp. 490 - 558

A finite-dimensional algebra A over an algebraically closed field K is called periodic if it is periodic under the action of the syzygy operator in the...

Periodic algebra | Surface algebra | Tame algebra | Syzygy | Self-injective algebra | STABLE EQUIVALENCE | BISERIAL ALGEBRAS | DEFORMED PREPROJECTIVE ALGEBRAS | GENERALIZED DYNKIN TYPE | SYMMETRIC ALGEBRAS | QUATERNION DEFECT-GROUPS | MATHEMATICS | POLYNOMIAL-GROWTH | CLUSTER ALGEBRAS | HOCHSCHILD COHOMOLOGY | SELF-INJECTIVE ALGEBRAS

Periodic algebra | Surface algebra | Tame algebra | Syzygy | Self-injective algebra | STABLE EQUIVALENCE | BISERIAL ALGEBRAS | DEFORMED PREPROJECTIVE ALGEBRAS | GENERALIZED DYNKIN TYPE | SYMMETRIC ALGEBRAS | QUATERNION DEFECT-GROUPS | MATHEMATICS | POLYNOMIAL-GROWTH | CLUSTER ALGEBRAS | HOCHSCHILD COHOMOLOGY | SELF-INJECTIVE ALGEBRAS

Journal Article

Communications in Algebra, ISSN 0092-7872, 07/2016, Volume 44, Issue 7, pp. 3069 - 3076

In this article, we study the existence of gradings on finite dimensional associative algebras. We prove that a connected algebra A does not have a nontrivial...

Unipotent morphisms | Graded algebras | Graded Morita equivalence | Quaternion defect groups | Secondary: 16W50 | Primary: 16A03 | MATHEMATICS | DIAGONALIZABLE DERIVATIONS | AUTOMORPHISMS

Unipotent morphisms | Graded algebras | Graded Morita equivalence | Quaternion defect groups | Secondary: 16W50 | Primary: 16A03 | MATHEMATICS | DIAGONALIZABLE DERIVATIONS | AUTOMORPHISMS

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 10/2010, Volume 138, Issue 10, pp. 3467 - 3479

Let k, and let G is a block of kG-modules. The description by Erdmann of the quiver and relations of the basic algebra of B whose value is either 0 or 1 if...

Homomorphisms | Algebra | Quaternions | Quaternion algebra | Mathematical rings | Mathematics | Vertices | MATHEMATICS | generalized quaternion defect groups | MATHEMATICS, APPLIED | Dihedral defect groups | projective general linear groups | Mathematics - Group Theory

Homomorphisms | Algebra | Quaternions | Quaternion algebra | Mathematical rings | Mathematics | Vertices | MATHEMATICS | generalized quaternion defect groups | MATHEMATICS, APPLIED | Dihedral defect groups | projective general linear groups | Mathematics - Group Theory

Journal Article

Algebras and Representation Theory, ISSN 1386-923X, 12/2013, Volume 16, Issue 6, pp. 1717 - 1732

We determine the numerical invariants of blocks with defect group $Q_{2^n}\times C_{2^m}$ and $SD_{2^n}\times C_{2^m}$ , where $Q_{2^n}$ denotes a quaternion...

Associative Rings and Algebras | 2-blocks | Ordinary weight conjecture | 20C20 | Semidihedral defect groups | Non-associative Rings and Algebras | Alperin’s Weight Conjecture | Commutative Rings and Algebras | Mathematics | Quaternion defect groups | 20C15

Associative Rings and Algebras | 2-blocks | Ordinary weight conjecture | 20C20 | Semidihedral defect groups | Non-associative Rings and Algebras | Alperin’s Weight Conjecture | Commutative Rings and Algebras | Mathematics | Quaternion defect groups | 20C15

Journal Article

Journal of Algebra, ISSN 0021-8693, 12/2015, Volume 443, pp. 200 - 269

Let A be an indecomposable representation-infinite tame finite-dimensional algebra of polynomial growth over an algebraically closed field. We prove that A is...

Periodic algebra | Orbit algebra | Syzygy | Galois covering | Tubular algebra | Polynomial growth | Self-injective algebra | GALOIS COVERINGS | SIMPLY CONNECTED ALGEBRAS | DEFORMED PREPROJECTIVE ALGEBRAS | GENERALIZED DYNKIN TYPE | SELFINJECTIVE ALGEBRAS | QUATERNION DEFECT-GROUPS | MATHEMATICS | TAME ALGEBRAS | HOCHSCHILD COHOMOLOGY | FINITE REPRESENTATION TYPE | WEAKLY SYMMETRIC ALGEBRAS | Computer science | Algebra

Periodic algebra | Orbit algebra | Syzygy | Galois covering | Tubular algebra | Polynomial growth | Self-injective algebra | GALOIS COVERINGS | SIMPLY CONNECTED ALGEBRAS | DEFORMED PREPROJECTIVE ALGEBRAS | GENERALIZED DYNKIN TYPE | SELFINJECTIVE ALGEBRAS | QUATERNION DEFECT-GROUPS | MATHEMATICS | TAME ALGEBRAS | HOCHSCHILD COHOMOLOGY | FINITE REPRESENTATION TYPE | WEAKLY SYMMETRIC ALGEBRAS | Computer science | Algebra

Journal Article

Journal of Algebra, ISSN 0021-8693, 08/2014, Volume 412, pp. 87 - 106

Let k be an algebraically closed field of positive characteristic, and let G be a finite group. Suppose B is a block of kG of infinite tame representation...

Tame blocks | Universal deformation rings | MATHEMATICS | ELLIPTIC-CURVES | MODULAR REPRESENTATIONS | THEOREM | DIHEDRAL DEFECT-GROUPS | CLASSIFICATION | SOURCE ALGEBRAS | QUATERNION | EQUIVALENCE | Mathematics - Representation Theory

Tame blocks | Universal deformation rings | MATHEMATICS | ELLIPTIC-CURVES | MODULAR REPRESENTATIONS | THEOREM | DIHEDRAL DEFECT-GROUPS | CLASSIFICATION | SOURCE ALGEBRAS | QUATERNION | EQUIVALENCE | Mathematics - Representation Theory

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 09/2014, Volume 142, Issue 9, pp. 3039 - 3047

is isomorphic to a power series algebra in one variable.]]>

Commutativity | Homomorphisms | Algebra | Mathematical theorems | Quotients | Mathematical rings | Power series | Cyclic blocks | Tame blocks | Defect groups | Generalized quaternion Sylow 2-subgroups | Universal deformation rings | cyclic blocks | MATHEMATICS | defect groups | generalized quaternion Sylow 2-subgroups | MATHEMATICS, APPLIED | MODULES | BLOCKS | tame blocks | Mathematics - Group Theory

Commutativity | Homomorphisms | Algebra | Mathematical theorems | Quotients | Mathematical rings | Power series | Cyclic blocks | Tame blocks | Defect groups | Generalized quaternion Sylow 2-subgroups | Universal deformation rings | cyclic blocks | MATHEMATICS | defect groups | generalized quaternion Sylow 2-subgroups | MATHEMATICS, APPLIED | MODULES | BLOCKS | tame blocks | Mathematics - Group Theory

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 12/2014, Volume 366, Issue 12, pp. 6507 - 6540

The versal deformation ring R(G,V) representation V encodes all isomorphism classes of lifts of V over complete local commutative Noetherian rings. We...

Brauer's generalized decomposition numbers | ENDO-TRIVIAL MODULES | DEFECT-GROUPS | CLASSIFICATION | Universal deformation rings | QUATERNION | COMPLETE-INTERSECTIONS | CHARACTERS | MATHEMATICS | generalized quaternion defect groups | ALGEBRAS | NEED | BLOCKS | tame blocks | semidihedral defect groups | FINITE GROUPS | dihedral defect groups | Mathematics - Group Theory

Brauer's generalized decomposition numbers | ENDO-TRIVIAL MODULES | DEFECT-GROUPS | CLASSIFICATION | Universal deformation rings | QUATERNION | COMPLETE-INTERSECTIONS | CHARACTERS | MATHEMATICS | generalized quaternion defect groups | ALGEBRAS | NEED | BLOCKS | tame blocks | semidihedral defect groups | FINITE GROUPS | dihedral defect groups | Mathematics - Group Theory

Journal Article

Journal of the European Mathematical Society, ISSN 1435-9855, 2013, Volume 15, Issue 1, pp. 157 - 177

Let G be a finite group with a Sylow 2-subgroup P which is either quaternion or semi-dihedral. Let k be an algebraically closed field of characteristic 2. We...

MATHEMATICS | MATHEMATICS, APPLIED | ALGEBRAS | ENDO-PERMUTATION MODULES | ALTERNATING GROUPS | DEFECT-GROUPS | FINITE-GROUPS | GROUPS-II | CLASSIFICATION | TRIVIAL MODULES

MATHEMATICS | MATHEMATICS, APPLIED | ALGEBRAS | ENDO-PERMUTATION MODULES | ALTERNATING GROUPS | DEFECT-GROUPS | FINITE-GROUPS | GROUPS-II | CLASSIFICATION | TRIVIAL MODULES

Journal Article

ALGEBRAS AND REPRESENTATION THEORY, ISSN 1386-923X, 12/2013, Volume 16, Issue 6, pp. 1717 - 1732

We determine the numerical invariants of blocks with defect group and , where denotes a quaternion group of order 2 (n) , denotes a cyclic group of order 2 (m)...

MATHEMATICS | 2-blocks | Ordinary weight conjecture | Semidihedral defect groups | CONJECTURES | Quaternion defect groups | Alperin's Weight Conjecture

MATHEMATICS | 2-blocks | Ordinary weight conjecture | Semidihedral defect groups | CONJECTURES | Quaternion defect groups | Alperin's Weight Conjecture

Journal Article

Algebras and Representation Theory, ISSN 1386-923X, 12/2013, Volume 16, Issue 6, pp. 1717 - 1732

Journal Article

Journal of Algebra, ISSN 0021-8693, 2003, Volume 269, Issue 2, pp. 652 - 668

Recently, a classification up to Morita equivalence of all weakly symmetric algebras which have tame representation type, simply connected Galois coverings and...

MATHEMATICS | REPRESENTATION TYPE | POLYNOMIAL-GROWTH | STABLE EQUIVALENCE | TRIVIAL EXTENSIONS | CATEGORIES | QUATERNION DEFECT-GROUPS

MATHEMATICS | REPRESENTATION TYPE | POLYNOMIAL-GROWTH | STABLE EQUIVALENCE | TRIVIAL EXTENSIONS | CATEGORIES | QUATERNION DEFECT-GROUPS

Journal Article

Journal of the Mathematical Society of Japan, ISSN 0025-5645, 01/2006, Volume 58, Issue 1, pp. 97 - 128

We determine the Calabi-Yau dimension of the stable module categories of all symmetric algebras of tame representation type over an algebraically closed field,...

Calabi-Yau dimension | Stable module category | Auslander-Reiten quiver | Selfinjective algebra | Periodic module | SIMPLY CONNECTED ALGEBRAS | PERIODIC MODULES | SELFINJECTIVE ALGEBRAS | CATEGORIES | QUATERNION DEFECT-GROUPS | EQUIVALENCE CLASSIFICATION | MATHEMATICS | POLYNOMIAL-GROWTH | periodic module | TRIVIAL EXTENSIONS | stable module category | SELF-INJECTIVE ALGEBRAS | selfinjective algebra

Calabi-Yau dimension | Stable module category | Auslander-Reiten quiver | Selfinjective algebra | Periodic module | SIMPLY CONNECTED ALGEBRAS | PERIODIC MODULES | SELFINJECTIVE ALGEBRAS | CATEGORIES | QUATERNION DEFECT-GROUPS | EQUIVALENCE CLASSIFICATION | MATHEMATICS | POLYNOMIAL-GROWTH | periodic module | TRIVIAL EXTENSIONS | stable module category | SELF-INJECTIVE ALGEBRAS | selfinjective algebra

Journal Article

Archiv der Mathematik, ISSN 0003-889X, 8/2003, Volume 81, Issue 2, pp. 142 - 154

We classify (up to Morita equivalence) all tame weakly symmetric finite dimensional algebras over an algebraically closed field having simply connected Galois...

16G60 | Mathematics | 16G20 | 16D50 | 16G70 | MATHEMATICS | POLYNOMIAL-GROWTH | QUATERNION DEFECT-GROUPS | TRIVIAL EXTENSIONS

16G60 | Mathematics | 16G20 | 16D50 | 16G70 | MATHEMATICS | POLYNOMIAL-GROWTH | QUATERNION DEFECT-GROUPS | TRIVIAL EXTENSIONS

Journal Article

Journal of Algebra, ISSN 0021-8693, 2004, Volume 271, Issue 2, pp. 798 - 826

We study the additive structure of Hochschild cohomology for blocks of modular group algebras of tame representation type. We give explicit formulae for the...

MATHEMATICS | ALGEBRAS | RING | 2-BLOCKS | FINITE-GROUPS | CLASSIFICATION | SYLOW 2-SUBGROUPS | QUATERNION | CATEGORIES | SEMIDIHEDRAL DEFECT GROUPS | EQUIVALENCE

MATHEMATICS | ALGEBRAS | RING | 2-BLOCKS | FINITE-GROUPS | CLASSIFICATION | SYLOW 2-SUBGROUPS | QUATERNION | CATEGORIES | SEMIDIHEDRAL DEFECT GROUPS | EQUIVALENCE

Journal Article

Journal of the Mathematical Society of Japan, ISSN 0025-5645, 10/2005, Volume 57, Issue 4, pp. 1077 - 1127

For a given finite dimensional k-algebra A which admits a presentation in the form R/G, where G is an infinite group of k-linear automorphisms of a locally...

Cohen-Macaulay module | Generalized tensor product | Galois covering | MATHEMATICS | REPRESENTATION-THEORY | POLYNOMIAL-GROWTH | POSETS | RINGS | SOCLE PROJECTIVE-MODULES | SELFINJECTIVE ALGEBRAS | SELF-INJECTIVE ALGEBRAS | QUATERNION DEFECT-GROUPS | generalized tensor product

Cohen-Macaulay module | Generalized tensor product | Galois covering | MATHEMATICS | REPRESENTATION-THEORY | POLYNOMIAL-GROWTH | POSETS | RINGS | SOCLE PROJECTIVE-MODULES | SELFINJECTIVE ALGEBRAS | SELF-INJECTIVE ALGEBRAS | QUATERNION DEFECT-GROUPS | generalized tensor product

Journal Article

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