(xy)z = x(yz)
``Finite-dimensional associative and Lie algebras''
[[xy]z]+[[zx]y]+[[yz]x]=0

Advisors :

Assistant Professors V.N.Zhelyabin, A.P.Pozhidaev

Novosibirsk State University

Content:

Part I: ``Finite-dimensional associative algebras''

SEMINAR 1
Associative Rings and algebras. Subrings, subalgebras, ideals.
Homomorphisms, factor-algebras, simple algebras. Regular Rings.

SEMINAR 2
Rings of Power-degrees series and Polynomial Rings.

SEMINAR 3
Nilpotence and nilpotent radical

SEMINAR 4
Quasiregular radical

SEMINAR 5,6
Semisimple algebras

SEMINAR 7
Simple algebras. Modules . Shur's Lemma. Density theorem.

SEMINAR 8
Simple algebras (continuation)

SEMINAR 9
Tensor products

SEMINAR 10
Tensor products (continuation),
Wedderburn-Malcev Theorem

SEMINAR 11
Wedderburn-Malcev Theorem (continuation)

Part II: ``Finite-dimensional Lie algebras''

SEMINAR 1
Lie algebras , subalgebras, ideals

SEMINAR 2
Derivations, Lie algebras of small dimensions

SEMINAR 3
Representations of Lie algebras

SEMINAR 4
Nilpotent Lie algebras

SEMINAR 5
Solvable Lie algebras

SEMINAR 6
Solvable and Nilpotent radicals

SEMINAR 7
Killing Form

SEMINAR 8
Extension of the base field