Related papers: A geometric model for the module category of a str…

In this paper we construct a Lie algebra representation of the algebraic string bracket on negative cyclic cohomology of an associative algebra with appropriate duality. This is a generalized algebraic version of the main theorem of [AZ]…

We study modular symmetries in non-supersymmetric heterotic string theories on toroidal backgrounds with Wilson line modulus, constructed by stringy Scherk-Schwartz compactification. In particular, we focus on a subgroup of the T-duality…

Thin coverings are a method of constructing graded-simple modules from simple (ungraded) modules. After a general discussion, we classify the thin coverings of (quasifinite) simple modules over associative algebras graded by finite abelian…

Let $G$ be a connected reductive algebraic group over a field of positive characteristic $p$ and denote by $\mathcal T$ the category of tilting modules for $G$. The higher Jones algebras are the endomorphism algebras of objects in the…

We develop silting theory of a noetherian algebra $\Lambda$ over a commutative noetherian ring $R$. We study mutation theory of $2$-term silting complexes of $\Lambda$, and as a consequence, we see that mutation exists. As in the case of…

We study the classification of submodules of module categories over monoidal categories, extending ideas of Coulembier on the classification of tensor ideals in monoidal categories. We develop a framework that applies to module categories…

This note provides a formula for the character of the Lie algebra of the fundamental group of a surface, viewed as a module over the symplectic group.

After introducing some motivations for this survey, we describe a formalism to parametrize a wide class of algebraic structures occurring naturally in various problems of topology, geometry and mathematical physics. This allows us to define…

Taking a Feynman categorical perspective, several key aspects of the geometry of surfaces are deduced from combinatorial constructions with graphs. This provides a direct route from combinatorics of graphs to string topology operations via…

This paper gives a construction, using heat kernels, of differential forms on the moduli space of metrised ribbon graphs, or equivalently on the moduli space of Riemann surfaces with boundary. The construction depends on a manifold with a…

In the authors book, Associative Algebraic Geometry, 2023, and the following article Shemes of Associative Algebras,\\ https://doi.org/10.48550/arXiv.2410.17703,2024, we use an algebraization of the semi-local formal moduli of simple…

In the 1980s, Harada introduced a new class of algebras now called Harada algebras. Harada algebras provides us with a rich source of Auslander's 1-Gorenstein algebras. In this paper, we have two main results about Harada algebras. The…

We use string-net models to accomplish a direct, purely two-dimensional, approach to correlators of two-dimensional rational conformal field theories. We obtain concise geometric expressions for the objects describing bulk and boundary…

We construct the skein category $\mathcal{S}$ of the annulus and show that it is equivalent to the affine Temperley-Lieb category of Graham and Lehrer. It leads to a skein theoretic description of the extended affine Temperley-Lieb…

We investigate a class of combinatory algebras, called ribbon combinatory algebras, in which we can interpret both the braided untyped linear lambda calculus and framed oriented tangles. Any reflexive object in a ribbon category gives rise…

Silting modules are abundant. Indeed, they parametrise the definable torsion classes over a noetherian ring, and the hereditary torsion pairs of finite type over a commutative ring. Also the universal localisations of a hereditary ring, or…

We show that the graded commutative ring structure of the Hochschild cohomology HH*(A) is trivial in case A is a triangular quadratic string algebra. Moreover, in case A isgentle, the Lie algebra structure on HH*(A) is also trivial.

Let $\Lambda$ be an algebra with a indecomposable projective-injective module. Adachi gave a method to construct the Hasse quiver of support $\tau$-tilting $\Lambda$-modules. In this paper, we will show that it can be restricted to…

This paper gives insight into intriguing connections between two apparently unrelated theories: the theory of skein modules of 3-manifolds and the theory of representations of groups into special linear groups of 2 by 2 matrices. Let R be a…

Given a grading by an abelian group G on a semisimple Lie algebra L over an algebraically closed field of characteristic 0, we classify up to isomorphism the simple objects in the category of finite-dimensional G-graded L-modules. The…