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We investigate the validity of the equivalence principle along paths in gravitational theories based on derivations of the tensor algebra over a differentiable manifold. We prove the existence of local bases, called normal, in which the…

General Relativity and Quantum Cosmology · Physics 2008-11-26 Bozhidar Z. Iliev

We define tilting subcategories in arbitrary exact categories to archieve the following. Firstly: Unify existing definitions of tilting subcategories to arbitrary exact categories. Discuss standard results for tilting subcategories:…

Representation Theory · Mathematics 2022-08-15 Julia Sauter

In this paper we introduce a new approach for organizing algebras of global dimension at most 2. We introduce the notion of cluster equivalence for these algebras, based on whether their generalized cluster categories are equivalent. We are…

Representation Theory · Mathematics 2012-03-08 Claire Amiot , Steffen Oppermann

We show that the Friedlander-Mazur conjecture holds for a complex smooth projective variety X of dimension three implies the standard conjectures hold for X. This together with a result of Friedlander yields the equivalence of the two…

Algebraic Geometry · Mathematics 2021-11-05 Jin Cao , Wenchuan Hu

In this paper we consider a construction in an arbitrary triangulated category T which resembles the notion of a Moore spectrum in algebraic topology. Namely, given a compact object C of T satisfying some finite tilting assumptions, we…

Category Theory · Mathematics 2010-06-03 David Pauksztello

In this paper we produce noncommutative algebras derived equivalent to deformations of schemes with tilting bundles. We do this in two settings, first proving that a tilting bundle on a scheme lifts to a tilting bundle on an infinitesimal…

Algebraic Geometry · Mathematics 2015-05-18 Joseph Karmazyn

Let A be a path A-infinity-algebra over a positively graded quiver Q. It is proved that the derived category of A is triangulated equivalent to the derived category of kQ, which is viewed as a dg algebra with trivial differential. The main…

Representation Theory · Mathematics 2016-11-01 Hao Su

In association with a finite dimensional algebra A of global dimension two, we consider the endomorphism algebra of A, viewed as an object in the triangulated hull of the orbit category of the bounded derived category, in the sense of…

Representation Theory · Mathematics 2011-10-25 Michael Barot , Sonia Trepode

In this paper we determine the derived representation type of quadratic string algebras and we prove that every derived tame quadratic string algebra whose quiver has cycles is derived equivalent to some skewed-gentle algebra.

Representation Theory · Mathematics 2020-11-17 Marlon Pimenta Fonseca

We prove that a certain pair of bimodules over two artin algebras gives rise to a triangle equivalence between the singularity categories of the two corresponding trivial extension algebras. Some consequences and an example are given.

Representation Theory · Mathematics 2016-06-28 Xiao-Wu Chen

We study the general rational trigonometry of a tetrahedron, based on quadrances, spreads and solid spreads, using vector products associated to an arbitrary symmetric bilinear form over a general field, not of characteristic two. This…

Metric Geometry · Mathematics 2021-08-17 Gennady A Notowidigdo , Norman J Wildberger

In this paper we construct a tilting sheaf for Severi-Brauer Varieties and Involution Varieties. This sheaf relates the derived category of each variety to the derived category of modules over a ring whose semisimple component consists of…

Algebraic Geometry · Mathematics 2012-04-04 Mark Blunk

In this paper, we construct derived equivalences between certain Nakayama algebras by using the notion of an S-family which is a family of objects in a triangulated category satisfying some axioms.

Rings and Algebras · Mathematics 2023-02-07 Taro Ueda

Three categories of algebras with morphisms generalising the usual set of algebra homomorphisms are described. The Sweedler product provides a hom-tensor equivalence relating these three categories, and a tool enabling the universal…

Rings and Algebras · Mathematics 2021-05-07 Marjorie Batchelor , Will Boulton , Daren Chen , Jonathan Rawlinson , Mustafa Warsi

We prove the equivalence of two tensor products over a category of W*-algebras with normal (not necessarily unital) *-homomorphisms, defined by Guichardet and Dauns, respectively. This structure differs from the standard tensor product…

Mathematical Physics · Physics 2017-12-21 Ryszard Paweł Kostecki , Tomasz Ignacy Tylec

We give a complete description of the derived equivalence normal forms of all one-parametric selfinjective algebras over algebraically closed fields which admit simply connected Galois coverings. As a consequence, a description of the…

Representation Theory · Mathematics 2007-05-23 Rafal Bocian , Thorsten Holm , Andrzej Skowronski

In this article, a new construction of derived equivalences is given. It relates different endomorphism rings and more generally cohomological endomorphism rings - including higher extensions - of objects in triangulated categories. These…

Representation Theory · Mathematics 2011-02-15 Wei Hu , Steffen Koenig , Changchang Xi

We classify gentle algebras defined by quivers with two cycles under derived equivalence in a non degenerate case, by using some combinatorial invariants constructed from the quiver with relations defining these algebras. We also present a…

Representation Theory · Mathematics 2008-08-15 Diana Avella-Alaminos

We assume given a smooth symplectic (in the algebraic sense) resolution $X$ of an affine algebraic variety $Y$, and we prove that, possibly after replacing $Y$ with an etale neighborhood of a point, the derived category of coherent sheaves…

Algebraic Geometry · Mathematics 2007-05-23 D. Kaledin

A simple graph is called triangular if every edge of it belongs to a triangle. We conjecture that any graphical degree sequence all terms of which are greater than or equal to 4 has a triangular realisation, and establish this conjecture…

Combinatorics · Mathematics 2023-04-03 Benjamin Egan , Yuri Nikolayevsky