Fundamental Investigations on the Isomorphism of Commutative Group Algebras in Bulgaria

The isomorphism problem of arbitrary algebraic structures plays always a central role in the study of a given algebraic object. In this paper we give the first investigations and also some basic results on the isomorphism problem of commutative group algebras in Bulgaria.

Isomorphism of Commutative Group Algebras of Finite Abelian Groups

Let a commutative ring R be a direct product of indecomposable rings with identity and let G be a finite abelian p-group. In the present paper we give a complete system of invariants of the group algebra RG of G over R when p is an invertible element in R. These investigations extend some classical results of Berman (1953 and 1958), Sehgal (1970) and Karpilovsky (1984) as well as a result of Mollov (1986).

Fundamental Investigations on the Unit Groups of Commutative Group Algebras in Bulgaria

In this paper we give the first investigations and also some basic results on the unit groups of commutative group algebras in Bulgaria. These investigations continue some classical results. Namely, it is supposed that the cardinality of the starting group is arbitrary.

The Variety of Leibniz Algebras Defined by the Identity x(y(zt)) ≡ 0

2000 Mathematics Subject Classification: Primary: 17A32; Secondary: 16R10, 16P99, 17B01, 17B30, 20C30

Involution Matrix Algebras – Identities and Growth

2000 Mathematics Subject Classification: 16R50, 16R10.

Invariants of Unipotent Transformations Acting on Noetherian Relatively Free Algebras

2000 Mathematics Subject Classification: 16R10, 16R30.

On Local Uniform Topological Algebras

2000 Mathematics Subject Classification: Primary 46H05, 46H20; Secondary 46M20.

q-Leibniz Algebras

2000 Mathematics Subject Classification: Primary 17A32, Secondary 17D25.

Semi-Symmetric Algebras: General Constructions. Part II

2000 Mathematics Subject Classification: 15A69, 15A78.

Normal and Normally Outer Automorphisms of Free Metabelian Nilpotent Lie Algebras

2000 Mathematics Subject Classification: 17B01, 17B30, 17B40.

Free Bicommutative Algebras

2000 Mathematics Subject Classification: Primary 17A50, Secondary 16R10, 17A30, 17D25, 17C50.

Outer endomorphisms of free metabelian Lie algebras

2000 Mathematics Subject Classification: 17B01, 17B30, 17B40.

Growth of some varieties of Leibniz-Poisson algebras

2010 Mathematics Subject Classification: 17A32, 17B63.

Tamed and Compatible Symplectic Forms on Four-Dimensional Almost Complex Lie Algebras

We are able to give a complete description of four-dimensional Lie algebras g which satisfy the tame-compatible question of Donaldson for all almost complex structures J on g are completely described. As a consequence, examples are given of (non-unimodular) four-dimensional Lie algebras with almost complex structures which are tamed but not compatible with symplectic forms.? Note that Donaldson asked his question for compact four-manifolds. In that context, the problem is still open, but it is believed that any tamed almost complex structure is in fact compatible with a symplectic form. In this presentation, I will define the basic objects involved and will give some insights on the proof. The key for the proof is translating the problem into a Linear Algebra setting. This is a joint work with Dr. Draghici.