Related papers: Left Ideal Preserving Maps on Triangular Algebras

Let S be a polynomial algebra over a field. If I is the edge ideal of a perfect semiregular tree, then we give precise formulas for values of depth, Stanley depth, projective dimension, regularity and Krull dimension of S/I.

We introduce a notion of left-symmetric Rinehart algebras, which is a generalization of a left-symmetric algebras. The left multiplication gives rise to a representation of the corresponding sub-adjacent Lie-Rinehart algebra. We construct…

Let $\mathcal{A}$ and $\mathcal{B}$ be two unital complex $\ast $-algebras such that $\mathcal{A}$ has a nontrivial projection. In this paper, we study the structure of bijective mappings $\Phi :\mathcal{A}\rightarrow \mathcal{B}$…

In this paper, we study admissible $\omega$-left-symmetric algebraic structures on $\omega$-Lie algebras over the complex numbers field $\mathbb C$. Based on the classification of $\omega$-Lie algebras, we prove that any perfect…

We investigate the notions of amenability and its related homological notions for a class of $I\times I$-upper triangular matrix algebra, say $UP(I,A)$, where $A$ is a Banach algebra equipped with a non-zero character. We show that…

Derivations extend the concept of differentiation from functions to algebraic structures as linear operators satisfying the Leibniz rule. In Lie algebras, derivations form a Lie algebra via the commutator bracket of linear endomorphisms.…

Let A be an idempotent algebra on a 3-element domain D that omits a G-set for a factor. Suppose A is not \alpha\beta-projective (for some alpha, beta subsets of D) and is not collapsible. It follows that A is switchable. We prove that, for…

Given a measure preserving transformation $T$ on a Lebesgue $\sigma$ algebra, a complete $T$ invariant sub $\sigma$ algebra is said to split if there is another complete $T$ invariant sub $\sigma$ algebra on which $T$ is Bernoulli which is…

Field equations for n-frames h_a{}^\mu that are possible in the theory of absolute parallelism (AP) are considered. The methods of compatibility (or formal integrability) theory enable us to find the non-Lagrangian equation having unusual…

Let $G$ be a finite group and $H$ a subgroup of $G$. Each left transversal (with identity) of $H$ in $G$ has a left loop (left quasigroup with identity) structure induced by the binary operation of $G$. We say two left transversals are…

We consider the problem of identifying exactly which AF-algebras are isomorphic to a graph C*-algebra. We prove that any separable, unital, Type I C*-algebra with finitely many ideals is isomorphic to a graph C*-algebra. This result allows…

An $n \times n$ matrix $A$ with real entries is said to be Schur stable if all the eigenvalues of $A$ are inside the open unit disc. We investigate the structure of linear maps on $M_n(\mathbb{R})$ that preserve the collection $\mathcal{S}$…

Motivated by the works of Wang [Y. Wang, \textit{Lie (Jordan) derivations of arbitrary triangular algebras,} Aequationes Mathematicae, \textbf{93} (2019), 1221-1229] and Moafian et al. [F. Moafian and H. R. Ebrahimi Vishki, \textit{Lie…

We show that every Lie algebra or superLie algebra has a canonical braiding on it, and that in terms of this its enveloping algebra appears as a flat space with braided-commuting coordinate functions. This also gives a new point of view…

Let $X$ be a real analytic orbifold. Then each stratum of $X$ is a subanalytic subset of $X$. We show that $X$ has a unique subanalytic triangulation compatible with the strata of $X$. We also show that every ${\rm C}^r$-orbifold, $1\leq…

Let $A$ be a split finite-dimensional associative unital algebra over a field. The first main result of this note shows that if the Ext-quiver of $A$ is a simple directed graph, then $HH^1(A)$ is a solvable Lie algebra. The second main…

The class of minimal non-elementary Lie algebras over a field F are studied. These are classified when F is algebraically closed and of characteristic different from 2,3. The solvable algebras in this class are also characterised over any…

A function on an algebra is congruence preserving if, for any congruence, it maps pairs of congruent elements onto pairs of congruent elements. We show that on the algebra of binary trees whose leaves are labeled by letters of an alphabet…

In this paper we investigate Lie bialgebra structures on a twisted Schr\"{o}dinger-Virasoro type algebra $\LL$. All Lie bialgebra structures on $\LL$ are triangular coboundary, which is different from the relative result on the original…

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…