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.

A C *-algebra A is called an ideal C * -algebra (or equally a dual algebra) if it is an ideal in its bidual A**. M.C.F. Berglund proved that subalgebras and quotients of ideal C*-algebras are also ideal C*-algebras, that a commutative C *-algebra A is an ideal C *-algebra if and only if it is isomorphicto C (Q) for some discrete space ?. We investigate ideal J*-algebras and show that the a...

Let g be a simple finite-dimensional Lie algebra and ĝκ, where κ is an invariant inner product on g, the corresponding affine Kac-Moody algebra. Consider the vacuum module Vκ over ĝκ (see Section 2 for the precise definitions). According to the results of [FF, Fr], the algebra of endomorphisms of Vκ is trivial, i.e., isomorphic to C, unless κ = κc, the critical value. The algebra Endĝκc Vκc is ...

The existing constructions of derived Lie and sh-Lie brackets involve multilinear maps that are used to define higher order differential operators. In this paper, we prove the equivalence of three different definitions of higher order operators. We then introduce a unifying theme for building derived brackets and show that two prevalent derived Lie bracket constructions are equivalent. Two basi...

let $a$ be a banach algebra and $x$ be a banach $a$-bimodule. then ${mathcal{s}}=a oplus x$, the $l^1$-direct sum of $a$ and $x$ becomes a module extension banach algebra when equipped with the algebra product $(a,x).(a',x')=(aa',ax'+xa').$ in this paper, we investigate biflatness and biprojectivity for these banach algebras. we also discuss on automatic continuity of derivations on ${mathcal{s...

The Clifford algebraic formulation of the Duffin–Kemmer–Petiau (DKP) algebras is applied to recast De Donder–Weyl Hamiltonian (DWH) theory as an description independent matrix representation DKP algebra. We show that DWH equations for antisymmetric fields arise out action algebra on certain invariant subspaces which carry representations fields. representation-free formula bracket associated wi...

Abstract Building on work of Gerstenhaber, we show that the space integrable derivations an Artin algebra forms a Lie algebra, and restricted if contains field characteristic . We deduce classes in (restricted) is invariant under derived equivalences, stable equivalences Morita type between self‐injective algebras. also provide negative answers to questions about posed by Linckelmann Farkas, Ge...

In this paper, extension of the EQ-logic by the ∆connective is introduced. The former is a new kind of many-valued logic which based on EQ-algebra of truth values, i.e. the algebra in which fuzzy equality is the fundamental operation and implication is derived from it. First, we extend the EQ-algebra by the ∆ operation and then introduce axioms and inference rules of EQ∆-logic. We also prove th...

In this paper we continue development of formal theory of a special class offuzzy logics, called EQ-logics. Unlike fuzzy logics being extensions of theMTL-logic in which the basic connective is implication, the basic connective inEQ-logics is equivalence. Therefore, a new algebra of truth values calledEQ-algebra was developed. This is a lower semilattice with top element endowed with two binary...

This paper presents a formalization of Grassmann-Cayley algebra [6] that has been done in the Coq [2] proof assistant. The formalization is based on a data structure that represents elements of the algebra as complete binary trees. This allows to define the algebra products recursively. Using this formalization, published proofs of Pappus’ and Desargues’ theorem [7,1] are interactively derived....