相关论文: The Auslander generators of the exterior algebra i…
Let $\Lambda$ be an artin algebra with representation dimension equal to three and $M$ an Auslander generator of $\Lambda$. We show how, under certain assumptions, we can mutate $M$ to get a new Auslander generator whose endomorphism ring…
We give analogues of the Auslander correspondence for two classes of triangulated categories satisfying certain finiteness conditions. The first class is triangulated categories with additive generators and we consider their endomorphism…
A $Z_3$-graded Hopf algebra structure of exterior algebra with two generators is introduced. Two covariant differential calculus on the $Z_3$-graded exterior algebra are presented. Using the generators and their partial derivatives a…
A version of Auslander theorem is proven for the following classes of noncommutative algebras: (a) noetherian PI local (or connected graded) algebras of finite injective dimension, (b) universal enveloping algebras of finite dimensional Lie…
The existence of invariant generators for distributions satisfying a compatibility condition with the symmetry algebra is proved.
We determine the minimal number of generators of the homological Goldman Lie algebra of a surface consisting of elements of the first homology group of the surface.
In this paper we exhibit a minimal set of generators form the annihilator of even neat elements of the exterior algebra of a vector space, when the base field is of positive characteristic and thus we prove the conjecture we established in…
A minimal (by inclusion) generating set for the algebra of semi-invariants of a quiver of dimension (2,...,2) is established over an infinite field of arbitrary characteristic. The mentioned generating set consists of the determinants of…
Over a field of characteristic 0, the algebra of invariants of several $n\times n$ matrices under simultaneous conjugation by $GL_n$ is generated by traces of products of generic matrices. In this paper we have found, in terms of…
It is a classical problem to compute a minimal set of invariant polynomial generating the invariant ring of a finite group as an algebra. We present here an algorithm for the computation of minimal generating sets in the non-modular case.…
Explicit generators are found for the group of automorphisms of the algebra of one-sided inverses of a polynomial algebra in $n$ variables. An analogue of the polynomial Jacobian homomorphism is found.
Let \Gamma be one of the N^2-dimensional bicovariant first order differential calculi on the orthogonal or symplectic quantum group O_q(N) or Sp_q(N). The parameter q is not a root of unity. We show that the second antisymmetrizer exterior…
We provide an explicit set of algebraically independent generators for the algebra of invariant differential operators on the Riemannian symmetric space associated with $\SL_n(\R)$.
In this paper we study the algebra of graph invariants, focusing mainly on the invariants of simple graphs. All other invariants, such as sorted eigenvalues, degree sequences and canonical permutations, belong to this algebra. In fact,…
In this paper, we consider the exterior algebra $\Lambda(W)$ of a polynomial $\mathrm{GL}(n)$-module $W$ and use previously developed methods to determine the Hilbert series of the algebra of invariants $\Lambda(W)^G$, where $G$ is one of…
Let $\Lambda$ be an $n$-Auslander algebra with global dimension $n+1$. In this paper, we prove that $\Lambda$ is representation-finite if and only if the number of non-isomorphic indecomposable $\Lambda$-modules with projective dimension…
A minimal system of homogeneous generating elements of the invariants algebra for the binary form of degree 7 is calculated.
The generators of the group of birational automorphisms of any Severi-Brauer surface non-isomorphic over an algebraically non-closed field to the projective plane are explicitly described.
It is well-known that every regular language admits a unique minimal deterministic acceptor. Establishing an analogous result for non-deterministic acceptors is significantly more difficult, but nonetheless of great practical importance. To…
The non-commutative differential calculus on the quantum groups $SL_q(N)$ is constructed. The quantum external algebra proposed contains the same number of generators as in the classical case. The exterior derivative defined in the…