Related papers: Finitely generated algebras with involution and th…
The starting point of this work is that the class of evolution algebras over a fixed field is closed under tensor product. This arises questions about the inheritance of properties from the tensor product to the factors and conversely. For…
The type and several invariant subspaces related to the upper annihilating series of finite-dimensional nilpotent evolution algebras are introduced. These invariants can be easily computed from any natural basis. Some families of nilpotent…
In this article we study algebraic structures of function spaces defined by graphs and state spaces equipped with Gibbs measures by associating evolution algebras. We give a constructive description of associating evolution algebras to the…
We introduce the notion of almost finite dimensionality of algebras and study its connection with the classical finiteness conditions.
A classification of (countable) direct limits of finite dimensional involution simple associative algebras over an algebraically closed field of arbitrary characteristic is obtained. This also classifies the corresponding dimension groups.…
We give a survey of recent results related to the problem of characterizing finite-dimensional division algebras by the set of isomorphism classes of their maximal subfields. We also discuss various generalizations of this problem and some…
It is shown that over an arbitrary countable field, there exists a finitely generated algebra that is nil, infinite dimensional, and has Gelfand-Kirillov dimension at most three.
We show that finitely generated cohomology is invariant under separable equivalences for all algebras. As a result, we obtain a proof of the finite generation of cohomology for finite symmetric tensor categories in characteristic zero, as…
Let $F$ be a field of characteristic not $2$ . An associative $F$-algebra $R$ gives rise to the commutator Lie algebra $R^{(-)}=(R,[a,b]=ab-ba).$ If the algebra $R$ is equipped with an involution $*:R\rightarrow R$ then the space of the…
We give a necessary and sufficient smoothness condition for the scheme parameterizing the n-dimensional representations of a finitely generated associative algebra over an algebraically closed field of characteristic zero. In particular,…
We observe that a finitely generated algebraic algebra R (over a field) is finite dimensional if and only if the associated graded ring grR is right noetherian, if and only if grR has right Krull dimension, if and only if grR satisfies a…
We study gradings by abelian groups on associative algebras with involution over an arbitrary field. Of particular importance are the fine gradings (that is, those that do not admit a proper refinement), because any grading on a…
We study polynomial identities of algebras with involution of nonassociative algebras over a field of characteristic zero. We prove that the growth of the sequence of $*$-codimensions of a finite-dimensional algebra is exponentially…
A graded-division algebra is an algebra graded by a group such that all nonzero homogeneous elements are invertible. This includes division algebras equipped with an arbitrary group grading (including the trivial grading). We show that a…
We compare some algebras appeared in the recent attempts to prove resolution of singularities in positive characteristic. We also construct an algebra which encodes the same information and it is equivalent, up to integral closure, to the…
Let $F$ be an algebraically closed field of characteristic zero, and $G$ be a finite abelian group. If $A=\oplus_{g\in G} A_g$ is a $G$-graded algebra, we study degree-inverting involutions on $A$, i.e., involutions $*$ on $A$ satisfying…
An extension of algebras is a homomorphism of algebras preserving identities. We use extensions of algebras to study the finitistic dimension conjecture over Artin algebras. Let $f: B \to A$ be an extension of Artin algebras. We denote by…
We show that the finitistic dimension conjecture holds for all finite dimensional algebras if and only if, for all finite dimensional algebras, the finitistic dimension of an algebra being finite implies that the finitistic dimension of its…
To use evolution algebras to model population dynamics that both allow extinction and introduction of certain gametes in finite generations, nilpotency must be built into the algebraic structures of these algebras with the entire algebras…
We describe gradings by finite abelian groups on the associative algebras of infinite matrices with finitely many nonzero entries, over an algebraically closed field of characteristic zero.