2000 Mathematics Subject Classification: Primary: 17A32; Secondary: 16R10, 16P99,
17B01, 17B30, 20C30
Let F be a field of characteristic zero. In this paper we study
the variety of Leibniz algebras 3N determined by the identity x(y(zt)) ≡ 0.
The algebras of this variety are left nilpotent of class not more than 3. We
give a complete description of the vector space of multilinear identities in
the language of representation theory of the symmetric group Sn
and Young
diagrams. We also...
This project was partially supported by RFBR, grants 99-01-00233, 98-01-01020 and
00-15-96128.
We study the asymptotic behaviour of numerical characteristics
of polynomial identities of Lie algebras over a field of characteristic 0. In
particular we investigate the colength for the cocharacters of polynilpotent
varieties of Lie algebras. We prove that there exist polynilpotent Lie varieties
with exponential and overexponential colength growth. We give the exact
asymptotics for the colength...
The contents of the article represents the minicourse which was delivered at the 7th conference "Geometry and Topology of Manifolds. The Mathematical Legacy of Charles Ehresmann", Będlewo (Poland), 8.05.2005 - 15.05.2005. The article includes the description of the so called Hirzebruch formula in different aspects which lead to a basic list of problems related to noncommutative geometry and topology. In conclusion, two new problems are presented: about almost flat bundles and about the Noether decomposition...
We study the asymptotic behaviour of the codimension sequence of varieties of Lie algebras variety over a field of characteristic zero. We construct an infinite series of such varieties with different fractional exponents. This extends the special cases known before. 2010 Mathematics Subject Classification: 17B01, 16R10, 16P90.
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