In this paper we develop new reduction techniques for testing the finiteness of finitistic dimension a finite dimensional algebra over field. Viewing latter as quotient path algebra, propose two operations on quiver namely arrow removal and vertex removal. The former gives rise to cleft extensions recollements. These provide us practical methods detect algebras dimension. We illustrate our with...

We study the derived critical locus of a function $f:[X/G]\to \mathbb{A}_{\mathbb{K}}^1$ on quotient stack smooth affine scheme $X$ by action group $G$. It is shown that $\mathrm{dCrit}(f) \simeq [Z/G]$ for $Z$, whose dg-algebra functions described explicitly. Our results generalize classical BV formalism in finite dimensions from Lie algebra to actions.

We present a general framework for Matrix theory compactified on a quotient space R/Γ, with Γ a discrete group of Euclidean motions in R. The general solution to the quotient conditions gives a gauge theory on a noncommutative space. We characterize the resulting noncommutative gauge theory in terms of the twisted group algebra of Γ associated with a projective regular representation. Present A...

Abstract We study subfields of quotient division algebras of domains of finite GK dimension and introduce a combinatorial property we call the straightening property. We show that many classes of algebras have this straightening property and show that if A is a domain of GK dimension d with this property that is not PI, then the maximal subfields of the quotient division algebra of A have trans...

We consider the relationship between derivations and local power series quotients for a locally multiplicatively convex Fr echet algebra (this includes the case of a Banach algebra). In x2 we derive necessary conditions for a commutative Fr echet algebra to have a local power series quotient. Our main result here is Proposition 2.6, which shows that if the generating element has nite closed des...

This paper introduces the concept of subalgebra and discusses some properties subalgebra. We also examine different types ideals how they behave. describe a homomorphism. Finally, we present quotient algebra discuss isomorphism theorems.

Operator quantization of constrained WZNW theories and coset constructions. Abstract Using two WZNW theories for Lie algebras g and h, h ⊂ g, we construct the associative quotient algebra which includes a class of g/h coset primary fields and currents. 1. In a recent article [1] for generic g/h coset conformal field theory [2] a class of Virasoro primary fields and currents was constructed.They...

In 2007 Phillips and Weaver showed that, assuming the Continuum Hypothesis, there exists an outer automorphism of the Calkin algebra. (The Calkin algebra is the algebra of bounded operators on a separable complex Hilbert space, modulo the compact operators.) In this paper we establish that the analogous conclusion holds for a broad family of quotient algebras. Specifically, we will show that as...

Let G be a locally compact Abelian group; I’ the dual group of G; CO(l_’)the algebra of continuous functions on r which vanish at infinity; CB(17)the continuous, bounded functions on r; M(G) the algebra of bounded Borel measures on G; Ll(G) the algebra of absolutely continuous measures; and M(G)A the algebra of l?ourier-Stielt jes transforms. Let E denote a compact subset of I’, and let A(E) be...

The topological filtration on K ′ 0 of a Severi-Brauer variety is computed if the quotient of its index and exponent is a squarefree number and for each prime p dividing this quotient the p -primary component of the corresponding division algebra is decomposable. This gives in particular a description of Ch for such varieties. Let D be a central simple algebra over a field F and X = SB(D) the S...