Predavanje profesora Yuri Bahturina




 Predavanje profesora Yuri Bahturina

Profesor Yuri Bahturin, predavač na Memorial University of Newfoundland, Canada, održaće predavanje pod nazivom On generic properties of nilpotent algebras u ponedeljak, 25.11. u 14h u sali 107a. U nastavku je sažetak predavanja.

We study general nilpotent algebras. The results obtained are new even for the classical algebras, such as associative or Lie algebras. We single out  certain generic properties of finite-dimensional algebras, mostly over infinite fields. The notion of being generic in the class of n-generated algebras of an arbitrary primitive class of nilpotent algebras appears naturally in the following way. On the set of the isomorphism classes of such algebras one can  introduce the structure of an algebraic variety, induced by the structure of Grassman varieties of ideals of algebras. As a result, the subsets are endowed with the dimensions as algebraic varieties. A subset Y of a set X of lesser dimension can be viewed as negligible in X. For example, if n is big enough, we determine that an  automorphism group of a generic algebra P consists of the automorphisms, which are scalar modulo P^2. Generic ideals are in I(P), the annihilator of P. In the case of classical nilpotent algebras as above, the generic algebras are graded by degrees with respect to some generating sets.

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