Related papers: Determinants of finite-dimensional algebras
A class of determinants is introduced. Different kind of mathematical objects, such as Fibonacci, Lucas, Tchebychev, Hermite, Laguerre, Legendre polynomials, sums and covergents are represented as determinants from this class. A closed…
Let $\mathbb{A}_n^m$ be an arbitrary $n$-dimensional commutative associative algebra over the field of complex numbers with $m$ idempotents. Let $e_1=1,e_2,e_3$ be elements of $\mathbb{A}_n^m$ which are linearly independent over the field…
We provide a clarification of the classification of two-dimensional algebras over an arbitrary base field. Using this clarification, we determine the number of non-isomorphic two-dimensional algebras over a finite field.
Source identities are fundamental identities between multivariable special functions. We give a geometric derivation of rational and trigonometric source identities. We also give a systematic derivation and extension of various determinant…
A notion of an algebroid - a generalization of a Lie algebroid structure is introduced. We show that many objects of the differential calculus on a manifold M associated with the canonical Lie algebroid structure on T^M can be obtained in…
The paper is devoted to classification problem of finite dimensional complex none Lie filiform Leibniz algebras. The motivation to write this paper is an unpublished yet result of J.R.Gomez, B.A.Omirov on necessary and sufficient conditions…
The coefficient algebra of a finite-dimensional Lie algebra on a finite-dimensional representation is defined as the subalgebra generated by all coefficients of the corresponding characteristic polynomial. We explore connections between…
We describe the variety of fixed points of a unipotent operator acting on the space of matrices. We compute the determinant and the rank of a generic (symmetric, or anti-symmetric) matrix in the fixed variety, yielding information about the…
We give a simplified complete proof for the classification of the selfinjective representation-finite algebras of finite dimension over an algebraically closed field. We explain the relations between the two different approaches and also to…
Under binary matrices we mean matrices whose entries take one of two values. In this paper, explicit formulae for calculating the determinant of some type of binary Toeplitz matrices are obtained. Examples of the application of the…
We observe algebraic derivations on an affine domain B defined over an algebraically closed field of characteristic 0, which are called locally finite derivations in commutative and non-commutative contexts in other references. We observe…
For any real division algebra A of finite dimension greater than one, the signs of the determinants of left multiplication and right multiplication by a non-zero element are shown to form an invariant of A, called its double sign. The…
We construct and study a class of algebras associated to generalized layered graphs, i.e. directed graphs with a ranking function on their vertices. Each finite directed acyclic graph admits countably many structures of a generalized…
For any finite dimensional basic associative algebra, we study the presentation spaces and their relation with the representation spaces. We prove two propositions about a general presentation, one on its subrepresentations and the other on…
It is known that any multiplication of a finite dimensional algebra is determined by a matrix of structural constants. In general, this is a cubic matrix. Difficulty of investigation of an algebra depends on the cubic matrix. Such a cubic…
One of the benefit properties implied by the extensionality axiom of Hilbert's epsilon calculus is that the calculus becomes complete with respect to the choice structures as semantics. Another implication of the axiom, discussed in the…
A description is given of those sequences ${\Bbb S}= (S(0),S(1),\dots,S(l))$ of simple modules over a finite dimensional algebra for which there are only finitely many uniserial modules with consecutive composition factors…
We diagonalize the Hilbert space of some subclass of the quasifinite module of the \Winf algebra. States are classified according to their eigenvalues for infinitely many commuting charges and the Young diagrams. The parameter dependence of…
The finitistic dimension conjecture asserts that any finite-dimensional algebra over a field should have finite finitistic dimension. Recently, this conjecture is reduced to studying finitistic dimensions for extensions of algebras. In this…
A number of categories is presented that are algebraically complete and cocomplete, i.e., every endofunctor has an initial algebra and a terminal coalgebra. For all finitary (and, more generally, all precontinuous) set functors the initial…