Related papers: A Finite Dimensional $A_{\infty}$ Algebra Example
In this article we prove various results about transferring or lifting $\mathrm{A}_\infty$-algebra structures along quasi-isomorphisms over a commutative ring.
We give an example of a finite dimensional algebra with infinite delooping level, based on an example of a semi-Gorenstein-projective module due to Ringel and Zhang.
In this paper we use finite vector spaces (finite dimension, over finite fields) as a non-standard computational model of linear logic. We first define a simple, finite PCF-like lambda-calculus with booleans, and then we discuss two finite…
An algebraic scheme is suggested in which discretized spacetime turns out to be a quantum observable. As an example, a toy model producing spacetimes of four points with different topologies is presented. The possibility of incorporating…
We give a full classification, up to equivalence, of finite-dimensional graded division algebras over the field of real numbers. The grading group is any abelian group.
Given a finite dimensional algebra $\Lambda$, we show that a frequently satisfied finiteness condition for the category ${\cal P}^{\infty}(\Lambda\rm{-mod})$ of all finitely generated (left) $\Lambda$-modules of finite projective dimension,…
We study maximal subalgebras of an arbitrary finite dimensional algebra over a field, and obtain full classification/description results of such algebras. This is done by first obtaining a complete classification in the semisimple case, and…
We investigate infinite versions of vector and affine space partition results, and thus obtain examples and a counterexample for a partition problem for relational structures. In particular we provide two (related) examples of an age…
Let $A$ be a bi-Koszul algebra, we describe all possible $A_\infty$-algebra structures on the Ext-algebra $E(A)$, and prove that $E(A)$ must be $[m_2, m_3]$-finitely generated. An equivalent description for a connected graded algebra to be…
We describe derivations of the Clifford algebra of a nondegenerate quadratic form on a countable dimensional vector space over an algebraically closed field of characteristic not equal to $2$. We also construct an algebraic automorphism of…
We provide a characterization of the finite dimensionality of vector spaces in terms of the right-sided invertibility of linear operators on them.
These notes deal with finite-dimensional normed algegras, some basic examples, and the definition of the spectrum.
For any increasing function $f: {\Bbb N} \rightarrow {\Bbb N}_{\ge 2}$ which takes only finitely many distinct values, a connected finite dimensional algebra $\Lambda$ is constructed, with the property that $\text{fin.dim}_n\, \Lambda =…
This article explores some simple examples of L-infinity algebras and the construction of miniversal deformations of these structures. Among other things, it is shown that there are two families of nonequivalent L-infinity structures on a…
Let A be a connected graded algebra and let E denote its Ext-algebra. There is a natural A-infinity algebra structure on E, and we prove that this structure is mainly determined by the relations of A. In particular, the coefficients of the…
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…
In this survey we discuss the results on the finitistic dimension of various stratified algebras. We describe what is already known, present some recent estimates, and list some open problems.
A finite-dimensional unital and associative algebra over $\mathbb{R}$, or what we shall call simply "an algebra" in this paper for short, generalities the construction by which we derive the complex numbers by "adjoining an element $i$" to…
We introduce a notion of elliptic differential graded Lie algebra. The class of elliptic algebras contains such examples as the algebra of differential forms with values in endomorphisms of a flat vector bundle over a compact manifold, etc.…
In this paper we define infinite-dimensional algebra and its representation, whose basis is naturally identified with semi-infinite configurations of the square ladder model. We also extrapolate the ideas for the cyclic 3-leg triangular…