Revaz KURDIANI
Razmadze Mathematical Institute of Georgian Academy of Sciences
Alexidze str. 1, Tbilisi, 380093, Republic of Georgia
E-mail: rezo@rmi.acnet.ge

Education

Tbilisi State University, Dept of Mathematics 1990-1995

Graduate Education

A. Razmadze Mathematical Institute of Georgian Academy of Sciences, Department of Algebra 1995-1998

Publications

1. Cohomology of Lie algebras in the tensor category of linear maps, Communications in Algebra, 27(10), (1999), 5033--5048.    dvi    ps

   Abstract

       In this paper we construct cohomology of Lie algebras in the tensor category of linear maps, which is obtained by iterated cone constructions starting from the ordinary Chevalley-Eilenberg complexes. Our cohomology theory turns out to be closely related to cohomology of local Lie algebras.
       Leibniz algebras are closely related to internal Lie algebras in the tensor category of linear maps. We prove the analog of Ado theorem for Lie algebras in the tensor category of linear maps, which yields a similar fact for Leibniz algebras. We construct the antiautomorphism of universal enveloping algebra of Leibniz algebra, which yields that the categories of Leibniz representations and corepresentations are isomorphic.

   
   
   
2. Universal central extensions of restricted Lie algebras, Proc. A. Razmadze Math. Inst. 121 (1999), 71--87.    dvi    ps

   Abstract

       In this paper we construct the universal central extension of restricted Lie algebra sl(A) . The kernel of it is computed. Moreover if g is a restricted Lie algebra, which is perfect as a Lie algebra we compute the kernel of the restricted universal central extension using the kernel of the universal central extension in the category of Lie algebras. As a consequence we get computations of the second homology groups for some class of restricted Lie algebras.