Zobrazeno 1 - 10
of 83
pro vyhledávání: '"Chuang, Joseph"'
Autor:
Chuang, Joseph, Lazarev, Andrey
The notion of one-sided localization in the homotopy invariant context is developed for dg algebras and dg categories. Applications include a simple construction of derived localization of dg algebras and dg categories, and a refinement of Drinfeld's
Externí odkaz:
http://arxiv.org/abs/2307.06043
Autor:
Chuang, Joseph, Lazarev, Andrey
We introduce the notion of a rank function on a triangulated category $\mathcal{C}$ which generalizes the Sylvester rank function in the case when $\mathcal{C}=\operatorname{Perf}(A)$ is the perfect derived category of a ring $A$. We show that rank f
Externí odkaz:
http://arxiv.org/abs/2101.01248
Autor:
Chuang, Joseph, Kessar, Radha
Publikováno v:
Proceedngs of 7ECM, European Mathematical Society (2018) 257--263
We show that perverse equivalences between module categories of finite-dimensional algebras preserve rationality. As an application, we give a connection between some famous conjectures from the modular representation theory of finite groups, namely
Externí odkaz:
http://arxiv.org/abs/1811.01000
DenseNets have been shown to be a competitive model among recent convolutional network architectures. These networks utilize Dense Blocks, which are groups of densely connected layers where the output of a hidden layer is fed in as the input of every
Externí odkaz:
http://arxiv.org/abs/1808.08308
We study Maurer-Cartan moduli spaces of dg algebras and associated dg categories and show that, while not quasi-isomorphism invariants, they are invariants of strong homotopy type, a natural notion that has not been studied before. We prove, in sever
Externí odkaz:
http://arxiv.org/abs/1802.02549
Autor:
Chuang, Joseph, Lazarev, Andrey
We introduce a certain differential graded bialgebra, neither commutative nor cocommutative, that governs perturbations of a differential on complexes supplied with an abstract Hodge decomposition. This leads to a conceptual treatment of the Homologi
Externí odkaz:
http://arxiv.org/abs/1703.05296
We provide closed formulas for a large subset of the canonical basis vectors of the Fock space representation of $U_q(\widehat{\mathfrak{sl}}_e)$. These formulas arise from parallelotopes which assemble to form polytopal complexes. The subgraphs of t
Externí odkaz:
http://arxiv.org/abs/1607.02803
Publikováno v:
Theory and Applications of Categories 31 (2016), 63-72
There is a general notion of the magnitude of an enriched category, defined subject to hypotheses. In topological and geometric contexts, magnitude is already known to be closely related to classical invariants such as Euler characteristic and dimens
Externí odkaz:
http://arxiv.org/abs/1505.04281
For any dg algebra $A$, not necessarily commutative, and a subset $S$ in $H(A)$, the homology of $A$, we construct its derived localisation $L_S(A)$ together with a map $A\to L_S(A)$, well-defined in the homotopy category of dg algebras, which posses
Externí odkaz:
http://arxiv.org/abs/1505.01146
Autor:
Chuang, Joseph, Tan, Kai Meng
We relate the canonical basis of the Fock space representation of the quantum affine algebra $U_q(\widehat{\mathfrak{gl}}_{n})$, as defined by Leclerc and Thibon, to the canonical basis of its restriction to $U_q(\mathfrak{sl}_{n})$, regarded as a ba
Externí odkaz:
http://arxiv.org/abs/1503.03616