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Mathematische Annalen, ISSN 0025-5831, 02/2017, Volume 367, Issue 1-2, pp. 121 - 134
The homotopy symmetric -algebras are those separable -algebras for which one can unsuspend in E-theory... 
46L80 | 19K99 | MATHEMATICS | ADMIT | BUNDLES | REPRESENTATIONS | ASYMPTOTIC MORPHISMS | NOVIKOV-CONJECTURE | KK-THEORY | HILBERT-SPACE | Algebra | Mathematics - Operator Algebras
Journal Article
Advances in Mathematics, ISSN 0001-8708, 04/2015, Volume 274, pp. 562 - 605
.... The simplicial category HoAlgCΔ gives us a particularly nice model of an (∞,1)-category of Cobar(C)-algebras. We show that the homotopy category of HoAlgC... 
Operads | Homotopy algebras | Higher categories | MATHEMATICS | REPRESENTATIONS | COMPLEXES | DEFORMATION-THEORY | Community colleges | Analysis | Algebra
Journal Article
Foundations of physics, ISSN 1572-9516, 2019, Volume 50, Issue 4, pp. 319 - 329
.... This paper is about the application of a new foundational programme in mathematics, namely homotopy type theory (HoTT... 
Univalence | Homotopy type theory | General covariance | PHYSICS, MULTIDISCIPLINARY | Hole argument
Journal Article
Communications in Mathematical Physics, ISSN 0010-3616, 1/2016, Volume 341, Issue 1, pp. 309 - 349
Journal Article
Journal für die reine und angewandte Mathematik (Crelles Journal), ISSN 0075-4102, 10/2018, Volume 2018, Issue 743, pp. 29 - 90
We show that certain tilting results for quivers are formal consequences of stability, and as such are part of a formal calculus available in any abstract stable homotopy theory... 
MATHEMATICS | K-THEORY | ALGEBRAS | MODULES | MODEL CATEGORY STRUCTURES | COMPLEXES
Journal Article
Differential Geometry and its Applications, ISSN 0926-2245, 10/2016, Volume 48, pp. 72 - 86
...∞-algebra, which we refer to as a homotopy Kirillov algebra. We are then led to higher Kirillov algebroids as higher generalisations of Jacobi algebroids... 
[formula omitted]-algebroids | Homotopy Poisson algebras | Kirillov structures | [formula omitted]-algebras | Homotopy BV-algebras | algebras | algebroids | MATHEMATICS | BRACKETS | MATHEMATICS, APPLIED | ALGEBRAS | REDUCTION | L-infinity-algebroids | MANIFOLDS | L-infinity-algebras | Algebra
Journal Article
Transactions of the American Mathematical Society, ISSN 0002-9947, 03/2016, Volume 368, Issue 3, pp. 2145 - 2184
We show that the canonical map from the associative operad to the unital associative operad is a homotopy epimorphism for a wide class of symmetric monoidal model categories... 
MATHEMATICS | unit | A-infinity algebra | REPRESENTATIONS | mapping space | MODEL CATEGORIES | Operad | NONSYMMETRIC OPERADS | DEFORMATION-THEORY | model category
Journal Article
Communications in Algebra, ISSN 0092-7872, 11/2016, Volume 44, Issue 11, pp. 4995 - 5003
Let A be an artin algebra. We show that the bounded homotopy category of finitely generated right A-modules has Auslander-Reiten triangles... 
Bounded homotopy categories | Gorenstein algebras | Auslander-Reiten triangles | Serre duality | Auslander–Reiten triangles | MATHEMATICS | ARTIN ALGEBRAS | SUBCATEGORIES | SPLIT-SEQUENCES | REPRESENTATION THEORY | Theorems | Algebra | Theorem proving | Categories | Triangles | Modules
Journal Article
ALGEBRA COLLOQUIUM, ISSN 1005-3867, 06/2019, Volume 26, Issue 2, pp. 195 - 230
The subject of this paper is strongly homotopy (SH) Lie algebras, also known as L-infinity-algebras... 
MATHEMATICS | MATHEMATICS, APPLIED | homotopical algebra | REPRESENTATIONS | PBW | L-infinity-algebra | Atiyah class
Journal Article
Differential Geometry and its Applications, ISSN 0926-2245, 06/2015, Volume 40, pp. 332 - 357
We show in this paper that the correspondence between 2-term representations up to homotopy and VB-algebroids, established in [6... 
VB-algebroids morphisms | Representations up to homotopy | Ideal systems | MATHEMATICS | MATHEMATICS, APPLIED | DRINFELD | GROUPOIDS | LIE BIALGEBROIDS
Journal Article
Journal of Pure and Applied Algebra, ISSN 0022-4049, 06/2016, Volume 220, Issue 6, pp. 2414 - 2433
In this paper, we show that the homotopy category of N-complexes of projective R-modules is triangle equivalent to the homotopy category of projective TN−1(R)-modules where TN−1(R... 
MATHEMATICS | MATHEMATICS, APPLIED | INFINITE QUIVERS. APPLICATIONS | HOMOLOGY | INJECTIVE REPRESENTATIONS
Journal Article
Mathematical proceedings of the Cambridge Philosophical Society, ISSN 0305-0041, 01/2015, Volume 158, Issue 1, pp. 155 - 191
I propose a definition of left/right connection along a strong homotopy Lie–Rinehart algebra. This allows me to generalise simultaneously representations up to homotopy of Lie algebroids and actions of L... 
MATHEMATICS | BRACKETS | COISOTROPIC SUBMANIFOLDS | COHOMOLOGY | GERSTENHABER ALGEBRAS | CATEGORY | DEFORMATIONS | MODULAR CLASS | BATALIN-VILKOVISKY ALGEBRAS | QUANTIZATION | Algebra | Calculus | Representations | Mathematical analysis | Manifolds (mathematics) | Lie groups
Journal Article
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, ISSN 0391-173X, 2017, Volume 17, Issue 1, pp. 143 - 185
.... In this article we develop methods for studying the low-dimensional homotopy groups of these spaces and of their sub-spaces X-r(irr... 
DEFORMATION K-THEORY | TOPOLOGY | MATHEMATICS | REPRESENTATIONS | MODULI SPACES | SURFACES
Journal Article
Geometry and Topology, ISSN 1465-3060, 01/2016, Volume 19, Issue 6, pp. 3105 - 3147
... (in orthogonal spectra) with triangulated homotopy categories. We show that the functors TR and TC are corepresentable in these categories... 
MATHEMATICS | FIELDS | K-THEORY
Journal Article
Journal of Algebra, ISSN 0021-8693, 2010, Volume 324, Issue 10, pp. 2718 - 2731
.... We give sufficient conditions under which a balanced pair of subcategories gives rise to a triangle-equivalence between two homotopy categories of complexes... 
Left-Gorenstein ring | Balanced pair | Relative derived category | Cotorsion triple | Homotopy category | MATHEMATICS | DIMENSIONS | PROJECTIVE-MODULES | TATE COHOMOLOGY | COMPLEXES | GORENSTEIN CATEGORIES
Journal Article
Advances in Mathematics, ISSN 0001-8708, 01/2019, Volume 341, pp. 367 - 439
...” of stable homotopy theory. In particular, we treat S-Lie algebras and their representations, characters, gln... 
Khovanov homology | Spectral algebra | Spectral representation theory | Homotopy categorification
Journal Article
Computers and Mathematics with Applications, ISSN 0898-1221, 2011, Volume 61, Issue 8, pp. 2330 - 2341
In this article, linear and nonlinear boundary value problems for fourth-order fractional integro-differential equations are solved by variational iteration method and homotopy perturbation method... 
Variational iteration method | Integro-differential equations | Boundary value problems | Homotopy perturbation method | Caputo fractional derivative | MATHEMATICS, APPLIED | NONLINEAR ANALYTICAL TECHNIQUE | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | Perturbation methods | Mathematical analysis | Nonlinearity | Mathematical models | Derivatives | Graphical representations | Iterative methods
Journal Article
International Journal of Geometric Methods in Modern Physics, ISSN 0219-8878, 05/2018, Volume 15, Issue 5
.... In this paper, we use the idea of representations up to homotopy of Lie algebroids to construct a same structure for hom-Lie algebroids and we will explain how representations up to homotopy... 
extensions | representation up to homotopy | representations | Hom-Lie algebroids | PHYSICS, MATHEMATICAL
Journal Article
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