Displaying similar documents to “Involution Matrix Algebras – Identities and Growth”

Symmetric Hochschild extension algebras

Yosuke Ohnuki, Kaoru Takeda, Kunio Yamagata (1999)

Colloquium Mathematicae

Similarity:

By an extension algebra of a finite-dimensional K-algebra A we mean a Hochschild extension algebra of A by the dual A-bimodule H o m K ( A , K ) . We study the problem of when extension algebras of a K-algebra A are symmetric. (1) For an algebra A= KQ/I with an arbitrary finite quiver Q, we show a sufficient condition in terms of a 2-cocycle for an extension algebra to be symmetric. (2) Let L be a finite extension field of K. By using a given 2-cocycle of the K-algebra L, we construct a 2-cocycle of...

Cartan matrices of selfinjective algebras of tubular type

Jerzy Białkowski (2004)

Open Mathematics

Similarity:

The Cartan matrix of a finite dimensional algebra A is an important combinatorial invariant reflecting frequently structural properties of the algebra and its module category. For example, one of the important features of the modular representation theory of finite groups is the nonsingularity of Cartan matrices of the associated group algebras (Brauer’s theorem). Recently, the class of all tame selfinjective algebras having simply connected Galois coverings and the stable Auslander-Reiten...

Dissident algebras

Ernst Dieterich (1999)

Colloquium Mathematicae

Similarity:

Given a euclidean vector space V = (V,〈〉) and a linear map η: V ∧ V → V, the anti-commutative algebra (V,η) is called dissident in case η(v ∧ w) ∉ ℝv ⊕ ℝw for each pair of non-proportional vectors (v,w) ∈ V 2 . For any dissident algebra (V,η) and any linear form ξ: V ∧ V → ℝ, the vector space ℝ × V, endowed with the multiplication (α,v)(β,w) = (αβ -〈v,w〉+ ξ(v ∧ w), αw + βv + η(v ∧ w)), is a quadratic division algebra. Up to isomorphism, each real quadratic division algebra arises in this...

On the representation type of tensor product algebras

Zbigniew Leszczyński (1994)

Fundamenta Mathematicae

Similarity:

The representation type of tensor product algebras of finite-dimensional algebras is considered. The characterization of algebras A, B such that A ⊗ B is of tame representation type is given in terms of the Gabriel quivers of the algebras A, B.

On Griess algebras.

Roitman, Michael (2008)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

Similarity: