20 research outputs found
Gradings on simple Jordan and Lie algebras
AbstractIn this paper we describe all group gradings by a finite Abelian group G of several types of simple Jordan and Lie algebras over an algebraically closed field F of characteristic zero
On the lifting of the Nagata automorphism
It is proved that the Nagata automorphism (Nagata coordinates, respectively)
of the polynomial algebra over a field cannot be lifted to a
-automorphism (-coordinate, respectively) of the free associative algebra
. The proof is based on the following two new results which have
their own interests: degree estimate of and tameness of
the automorphism group .Comment: 15 page
Двухмерное биномиальное распределение
We consider a model of two-dimensional random vector with dependent binomial marginals.The distribution for constructed model is determined.Рассматривается модель двухмерного случайного вектора с зависимыми, биномиально распределёнными маргиналами, определяется закон распределения построенной модели
The Freiheitssatz for Generic Poisson Algebras
We prove the Freiheitssatz for the variety of generic Poisson algebras
Hopf algebras in non-associative Lie theory
We review the developments in the Lie theory for non-associative products from 2000 to date and describe the current understanding of the subject in view of the recent works, many of which use non-associative Hopf algebras as the main tool
Nilpotent Sabinin algebras
In this paper we establish several basic properties of nilpotent Sabinin algebras. Namely, we show that nilpotent Sabinin algebras (1) can be integrated to produce nilpotent loops, (2) satisfy an analogue of the Ado theorem, (3) have nilpotent Lie envelopes. We also give a new set of axioms for Sabinin algebras. These axioms reflect the fact that a complementary subspace to a Lie subalgebra in a Lie algebra is a Sabinin algebra. Finally, we note that the non-associative version of the Jennings theorem produces a version of the Ado theorem for loops whose commutator-associator filtration is of finite length. © 2014
Primitive ideals and automorphisms of quantum matrices.
Let K be a field and q be a nonzero element of K that is not a root of unity. We give a criterion for (0) to be a primitive ideal of the algebra O-q(M-m,M-n) of quantum matrices. Next, we describe all height one primes of these two problems are actually interlinked since it turns out that (0) is a primitive ideal of O-q(M-m,M-n) whenever O-q(M-m,M-n) has only finitely many height one primes. Finally, we compute the automorphism group of O-q(M-m,M-n) in the case where m not equal n. In order to do this, we first study the action of this group on the prime spectrum of O-q(M-m,M-n). Then, by using the preferred basis of O-q(M-m,M-n) and PBW bases, we prove that the automorphism group of O-q(M-m,M-n) is isomorphic to the torus (K*)(m+n=1) when m not equal n and (m, n) not equal (1, 3) (3, 1)