共查询到20条相似文献,搜索用时 46 毫秒
1.
A. V. Leont’ev 《Russian Mathematics (Iz VUZ)》2010,54(3):12-18
We obtain the lower bounds for the tensor rank for the class of nilpotent and solvable Lie algebras (in terms of dimensions
of certain quotient algebras). These estimates, in turn, give lower bounds for the complexity of algebraic algorithms for
this class of algebras. We adduce examples of attainable estimates for nilpotent Lie algebras of various dimensions. 相似文献
2.
A. D. Uadilova 《Russian Mathematics (Iz VUZ)》2010,54(8):57-66
The main object of study are ternary algebras, i.e., algebras with a trilinear operation. In this class we study finitely
generated algebras and their growth, as well as the growth of codimensions of absolutely free algebras and some other varieties.
For these purposes we use ordinary generating functions and exponential generating functions (the complexity functions). In
the classes of absolutely free, free symmetric, free antisymmetric, and some other algebras we study left nilpotent and completely
left nilpotent algebras and varieties. The obtained results are equivalent to the enumeration of ternary trees which contain
no forbidden subtrees of a special kind. As the main result, we prove that the complexity functions of the varieties of completely
left nilpotent and left nilpotent ternary algebras are algebraic. 相似文献
3.
Maria V. Milentyeva 《代数通讯》2013,41(4):1141-1154
We obtain the functions that bound the dimensions of finite dimensional nilpotent associative or Lie algebras of class 2 over an algebraically closed field in terms of the dimensions of their commutative subalgebras. As a result, we also compute a similar function for complex nilpotent Lie groups of class 2. 相似文献
4.
In [1], the second de Rham cohomology groups of nilpotent orbits in all the complex simple Lie algebras are described. In this paper we consider non-compact non-complex exceptional Lie algebras, and compute the dimensions of the second cohomology groups for most of the nilpotent orbits. For the rest of cases of nilpotent orbits, which are not covered in the above computations, we obtain upper bounds for the dimensions of the second cohomology groups. 相似文献
5.
Relations between Goldie conditions of a semiprime algebraR and its subalgebraR
d of constants under an algebraic derivation are studied. The results obtained are applied to actions of finite dimensional
solvable Lie algebras on associative algebras with no non-zero nilpotent elements.
Supported by KBN Grant No. 2 2012 91 02.
Supported by KBN Grant No. 2 2047 91 02. 相似文献
6.
Summary We describe the class of complex filiform nilpotent Lie algebras provided with a not trivial external torus of derivations.
We prove also that, for dimensions greater than 8, any algebraic irreducible component of the variety of complex nilpotent
filiform laws of Lie algebra contains an open set whose elements are characteristically nilpotent laws.
This article was processed by the author using the Springer-Verlag TEXP Jour1g macro package 1991. 相似文献
This article was processed by the author using the Springer-Verlag TEXP Jour1g macro package 1991. 相似文献
7.
The notion of geometrical equivalence of two algebras, which is basic for this paper, is introduced in [5], [6]. It is motivated in the framework of universal algebraic geometry, in which algebraic varieties are considered in arbitrary varieties of algebras. Universal algebraic geometry (as well as classic algebraic geometry) studies systems of equations and its geometric images, i.e., algebraic varieties, consisting of solutions of equations. Geometrical equivalence of algebras means, in some sense, equal possibilities for solving systems of equations. In this paper we consider results about geometrical equivalence of algebras, and special attention is paied on groups (abelian and nilpotent). 相似文献
8.
Ivan Kaygorodov Mykola Khrypchenko Yury Popov 《Journal of Pure and Applied Algebra》2021,225(6):106625
We give algebraic and geometric classifications of 4-dimensional complex nilpotent terminal algebras. Specifically, we find that, up to isomorphism, there are 41 one-parameter families of 4-dimensional nilpotent terminal (non-Leibniz) algebras, 18 two-parameter families of 4-dimensional nilpotent terminal (non-Leibniz) algebras, 2 three-parameter families of 4-dimensional nilpotent terminal (non-Leibniz) algebras, complemented by 21 additional isomorphism classes (see Theorem 13). The corresponding geometric variety has dimension 17 and decomposes into 3 irreducible components determined by the Zariski closures of a one-parameter family of algebras, a two-parameter family of algebras and a three-parameter family of algebras (see Theorem 15). In particular, there are no rigid 4-dimensional complex nilpotent terminal algebras. 相似文献
9.
A non-nilpotent variety of algebras is almost nilpotent if any proper subvariety is nilpotent. Let the base field be of characteristic zero. It has been shown that for associative or Lie algebras only one such variety exists. Here we present infinite families of such varieties. More precisely we shall prove the existence of1) a countable family of almost nilpotent varieties of at most linear growth and2) an uncountable family of almost nilpotent varieties of at most quadratic growth. 相似文献
10.
I. N. Ponomarenko 《Journal of Mathematical Sciences》1996,79(3):1105-1114
In this paper, we study the computation complexity of some algebraic combinatorial problems that are closely associated with
the graph isomorphism problem. The key point of our considerations is a relation algebra which is a combinatorial analog of
a cellular algebra. We present upper bounds on the complexity of central algorithms for relation algebras such as finding
the standard basis of extensions and intersection of relation algebras. Also, an approach is described to the graph isomorphism
problem involving Schurian relation algebras (these algebras arise from the centralizing rings of permutation groups). We
also discuss a number of open problems and possible directions for further investigation. Bibliography: 18 titles.
Translated by I. N.Ponomarenko.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol 202, 1992, pp. 116–134. 相似文献
11.
Marco A. S. Trindade Eric Pinto J. D. M. Vianna 《Advances in Applied Clifford Algebras》2016,26(2):771-792
The aim of this paper is to present a general algebraic formulation for the decoherence-free subspaces (DFSs). In order to build the DFSs we consider the tensor product of Clifford algebras and left minimal ideals. States, error operators and projection operators are defined in a purely algebraic point of view. For this purpose, we initially generalize some results of Pauli and Artin about semisimple algebras. Then we derive orthogonality theorems for associative algebras analogous to theorems for finite groups. Some advantages and perspectives are also discussed. 相似文献
12.
Sergei R. Sverchkov 《Central European Journal of Mathematics》2014,12(11):1687-1699
We prove that the variety of Lie algebras arising from splicing operation coincides with the variety CM of centreby-metabelian Lie algebras. Using these Lie algebras we find the minimal dimension algebras generated the variety CM and the variety of its associative envelope algebras. We study the splicing n-ary operation. We show that all n-ary (n > 2) commutator algebras arising from this operation are nilpotent of index 3. We investigate the generalization of the splicing n-ary operation, and we formulate a series of open problems. 相似文献
13.
14.
Pavel Kolesnikov 《Algebras and Representation Theory》2013,16(6):1521-1539
In this paper, we consider graded associative conformal algebras. The class of these objects includes pseudo-algebras over non-cocommutative Hopf algebras of regular functions on some linear algebraic groups. In particular, an associative conformal algebra which is graded by a finite group Γ is a pseudo-algebra over the coordinate Hopf algebra of a linear algebraic group G such that the identity component G 0 is the affine line and G/G 0???Γ. A classification of simple and semisimple graded associative conformal algebras of finite type is obtained. 相似文献
15.
Karl-Hermann Neeb 《manuscripta mathematica》2001,104(3):359-381
In this paper we essentially classify all locally finite Lie algebras with an involution and a compatible root decomposition
which permit a faithful unitary highest weight representation. It turns out that these Lie algebras have many interesting
relations to geometric structures such as infinite-dimensional bounded symmetric domains and coadjoint orbits of Banach–Lie
groups which are strong K?hler manifolds. In the present paper we concentrate on the algebraic structure of these Lie algebras,
such as the Levi decomposition, the structure of the almost reductive and locally nilpotent part, and the structure of the
representation of the almost reductive algebra on the locally nilpotent ideal.
Received: 2 August 2000 / Revised version: 10 January 2001 相似文献
16.
The only known examples of Anosov diffeomorphisms are hyperbolic automorphisms of infranilmanifolds, and the existence of such automorphisms is a really strong condition on the rational nilpotent Lie algebra determined by the lattice, so called an Anosov Lie algebra. We prove that n⊕?⊕n (s times, s≥2) has an Anosov rational form for any graded real nilpotent Lie algebra n having a rational form. We also obtain some obstructions for the types of nilpotent Lie algebras allowed, and use the fact that the eigenvalues of the automorphism are algebraic integers (even units) to show that the types (5,3) and (3,3,2) are not possible for Anosov Lie algebras. 相似文献
17.
Ivan Losev 《Advances in Mathematics》2011,(6):1741
A W-algebra is an associative algebra constructed from a reductive Lie algebra and its nilpotent element. This paper concentrates on the study of 1-dimensional representations of W-algebras. Under some conditions on a nilpotent element (satisfied by all rigid elements) we obtain a criterium for a finite dimensional module to have dimension 1. It is stated in terms of the Brundan–Goodwin–Kleshchev highest weight theory. This criterium allows to compute highest weights for certain completely prime primitive ideals in universal enveloping algebras. We make an explicit computation in a special case in type E8. Our second principal result is a version of a parabolic induction for W-algebras. In this case, the parabolic induction is an exact functor between the categories of finite dimensional modules for two different W-algebras. The most important feature of the functor is that it preserves dimensions. In particular, it preserves one-dimensional representations. A closely related result was obtained previously by Premet. We also establish some other properties of the parabolic induction functor. 相似文献
18.
Lisa Hefendehl-Hebeker 《manuscripta mathematica》1983,41(1-3):173-216
Assuming properties, which are essential for division algebras, but mostly invariant to extensions of the ground field, we investigate the structure of quadratic division algebras of dimension four over an arbitrary field of characteristic not two. We relate the size of the group of automorphisms of such an algebra A to algebraic laws valid in A, characterize Lie-admissibility by means of the skew-commutative vector algebra of A and outline the possibilities of describing A by irreducible identities of degree 3. Some results of the last chapter apply to arbitrary dimensions. We show, that a simple quadratic algebra with the right (left) inverse property for invertible elements is a composition algebra. Finally we conclude, that a quadratic division algebra of dimension four with a right (left) nucleus different from the center is associative. 相似文献
19.
20.
Wenxue Huang 《Linear and Multilinear Algebra》1996,40(4):303-309
Let A be a linear (i.e., finite-dimensional) associative algebra with unity defined over K, an algebraically closed field. Then A with respect to its multiplication is an algebraic monoid over k, denoted by AM, and with respect to the the bracket forms a Lie algebra over K, denoted by AL. The following theorem is established AM is nilpotent as an algebraic monoid (equivalentlyAL is so as a Lie algebra) if and only if the set of idempotents of A is finite if and only if all irreducible closed submonoids of codimension 1 are nilpotent. 相似文献