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Isomorphism of Commutative Modular Group Algebras

Danchev, P. (1997)

Serdica Mathematical Journal

∗ The work was supported by the National Fund “Scientific researches” and by the Ministry of Education and Science in Bulgaria under contract MM 70/91.Let K be a field of characteristic p > 0 and let G be a direct sum of cyclic groups, such that its torsion part is a p-group. If there exists a K-isomorphism KH ∼= KG for some group H, then it is shown that H ∼= G. Let G be a direct sum of cyclic groups, a divisible group or a simply presented torsion abelian group. Then KH ∼= KG as K-algebras...

Isomorphisms between graded Frobenius algebras constructed from twisted superpotentials

Xuejun Xia, Libin Li (2022)

Czechoslovak Mathematical Journal

In order to distinguish the connected graded Frobenius algebras determined by different twisted superpotentials, we introduce the nondegeneracy of twisted superpotentials. We give the sufficient and necessary condition for connected graded Frobenius algebras determined by two nondegenerate twisted superpotentials to be isomorphic. As an application, we classify the connected ℤ -graded Frobenius algebra of length 3, whose dimension of the degree 1 is 2.

Isomorphisms between representations of algebras.

Manuel Saorín (1992)

Publicacions Matemàtiques

In this paper we study the precise relation between two representations of a given split finite basic dimensional algebra A as a factor of the free path algebra over its quiver (A). After defining the notion of strongly acyclic quiver, we apply the results obtained to develop a method of calculating the group Aut(A)/Inn(A) in the case when (A) is strongly acyclic.

Isorings and related isostructures

Raúl M. Falcón, Juan Núñez Valdés (2005)

Bollettino dell'Unione Matematica Italiana

The main goal of this paper is to give a mathematical foundation, serious and consistent, to some parts of Santilli’s isotheory. We study the isotopic liftings of rings, subrings and ideals, and we also introduce the concept of quotient isoring. By using the isoproduct model, necessary conditions assuring the existence of such isostructures are given. Such conditions are based on the inner laws which originate the associated elements of isotopy. These elements will allow to extend, from a different...

Iterated coil enlargements of algebras

Bertha Tomé (1995)

Fundamenta Mathematicae

Let Λ be a finite-dimensional, basic and connected algebra over an algebraically closed field, and mod Λ be the category of finitely generated right Λ-modules. We say that Λ has acceptable projectives if the indecomposable projective Λ-modules lie either in a preprojective component without injective modules or in a standard coil, and the standard coils containing projectives are ordered. We prove that for such an algebra Λ the following conditions are equivalent: (a) Λ is tame, (b) the Tits form...

Iterated tilted and tilted stably hereditary algebras

Jessica Lévesque (2003)

Colloquium Mathematicae

We prove that a stably hereditary bound quiver algebra A = KQ/I is iterated tilted if and only if (Q,I) satisfies the clock condition, and that in this case it is of type~Q. Furthermore, A is tilted if and only if (Q,I) does not contain any double-zero.

Jordan- and Lie geometries

Wolfgang Bertram (2013)

Archivum Mathematicum

In these lecture notes we report on research aiming at understanding the relation beween algebras and geometries, by focusing on the classes of Jordan algebraic and of associative structures and comparing them with Lie structures. The geometric object sought for, called a generalized projective, resp. an associative geometry, can be seen as a combination of the structure of a symmetric space, resp. of a Lie group, with the one of a projective geometry. The text is designed for readers having basic...

Jordan automorphisms of triangular algebras. II

Driss Aiat Hadj Ahmed, Rachid Tribak (2015)

Commentationes Mathematicae Universitatis Carolinae

We give a sufficient condition under which any Jordan automorphism of a triangular algebra is either an automorphism or an anti-automorphism.

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