Related papers: Derived equivalences and delooping levels

We define a transcendence degree for division algebras, by modifying the lower transcendence degree construction of Zhang. We show that this invariant has many of the desirable properties one would expect a noncommutative analogue of the…

We relate the notions of BB-tilting and perverse derived equivalence at a vertex. Based on these notions, we define mutations of algebras, leading to derived equivalent ones. We present applications to endomorphism algebras of…

We develop a deformation theory for finite-dimensional left-symmetric color algebras, which can be used to construct new algebraic structures and interpret left-symmetric color cohomology spaces of lower degrees. We explore equivalence…

We study the algebraic rank of a divisor on a graph, an invariant defined using divisors on algebraic curves dual to the graph. We prove it satisfies the Riemann-Roch formula, a specialization property, and the Clifford inequality. We prove…

Finite differences have been widely used in mathematical theory as well as in scientific and engineering computations. These concepts are constantly mentioned in calculus. Most frequently-used difference formulas provide excellent…

In Part I of this paper, we introduced a class of certain algebras of finite dimension over a field. All these algebras are split, symmetric and local. Here we continue to investigate their Loewy structure. We show that in many cases their…

Let $A$ be a finite-dimensional $k$-algebra and $K/k$ be a finite separable field extension. We prove that $A$ is derived equivalent to a hereditary algebra if and only if so is $A\otimes_kK$.

In low dimensional topology, we have some invariants defined by using solutions of some nonlinear elliptic operators. The invariants could be understood as Euler class or degree in the ordinary cohomology, in infinite dimensional setting.…

We present a general construction of the derived category of an algebra over an operad and establish its invariance properties. A central role is played by the enveloping operad of an algebra over an operad.

The notion of a derived A-infinity algebra, considered by Sagave, is a generalization of the classical notion of A-infinity algebra, relevant to the case where one works over a commutative ring rather than a field. We initiate a study of…

Let X be an algebraic variety with an action of an algebraic group G. Suppose X has a full exceptional collection of sheaves, and these sheaves are invariant under the action of the group. We construct a semiorthogonal decomposition of…

Let $\mathscr{A}$ and $\mathscr{B}$ be two connected cochain DG algebra such that $\mathscr{A}^{\#}=\mathscr{B}^{\#}$ and the cohomology rings $H(\mathscr{A})$ and $H(\mathscr{B})$ are isomorphic. We give examples to show that $\mathscr{A}$…

Classical W-algebras in higher dimensions have been recently constructed. In this letter we show that there is a finitely generated subalgebra which is isomorphic to the algebra of local diffeomorphisms in D dimensions. Moreover, there is a…

Let $X$ be an algebraic stack with quasi-affine diagonal of finite type over a field $k$ of characteristic $0$. We extend the well-known equivalence $\mathsf{D}^+(\mathsf{QCoh}(X)) \simeq \mathsf{D}_{\mathrm{qc}}^+(X)$ to unbounded derived…

Let C be a separable unital C*-algebra, not isomorphic to the complex numbers, equipped with a faithful tracial state. Let A be a unital direct limit of one dimensional NCCW complexes, also equipped with a faithful tracial state. Suppose…

Consider an external product of a higher cycle and a usual cycle which is algebraically equivalent to zero. Assume there exists an algebraically closed subfield k such that the higher cycle and its ambient variety are defined over k, but…

We consider families of chain-cochain infinite complexes $\mathcal C$ of spaces with elements depending on a number of parameters, and endowed with a converging associative multiple product. The existence of left/right local/non-local…

This lecture consists of two sections. In section 1 we consider the simplest version of a q-deformed Heisenberg algebra as an example of a noncommutative structure. We first derive a calculus entirely based on the algebra and then formulate…

Detailed mappings between zero-curvture equations for prolongation structures of nonlinear pde's and Estabrook-Wahlquist algorithms for same are given. The differences are exemplified by studies of the sine-Gordon equation. An example where…

Inspired by the commutator and anticommutator algebras derived from algebras graded by groups, we introduce noncommutatively graded algebras. We generalize various classical graded results to the noncommutatively graded situation concerning…