相关论文: Higher polyhedral K-groups

In this article, we extend our preceding studies on higher algebraic structures of (co)homology theories defined by a left bialgebroid (U,A). For a braided commutative Yetter-Drinfel'd algebra N, explicit expressions for the canonical…

In this paper we deduce a graded version of Quillen--Suslin's Local-Global Principle for the traditional classical groups, viz. general linear, symplectic and orthogonal groups and establish its equivalence of the normality property of the…

This paper lays out the foundations of graded $K$-theory for Leavitt algebras associated with higher-rank graphs, also known as Kumjian-Pask algebras, establishing it as a potential tool for their classification. For a row-finite $k$-graph…

Elements of the tropical vertex group are formal families of symplectomorphisms of the 2-dimensional algebraic torus. Commutators in the group are related to Euler characteristics of the moduli spaces of quiver representations and the…

The classification of the unitary irreducible representations of symmetry groups is a cornerstone of modern quantum physics, as it provides the fundamental building blocks for constructing the Hilbert spaces of theories admitting these…

We consider algebras over a field K defined by a presentation K <x_1,..., x_n : R >, where $R$ consists of n choose 2 square-free relations of the form x_i x_j = x_k x_l with every monomial x_i x_j, i different from j, appearing in one of…

We prove that the relative K-groups associated with a nilpotent extension of Z/p^N Z-algebras and the bi-relative K-groups associated with a Milnor square of Z/p^N Z-algebras are p-primary torsion groups of bounded exponent. We also show…

We calculate explicitly cohomologies of the lattices over the Kleinian 4-group belonging to the regular components of the Auslander-Reiten quiver as well as of their dual modules. The result is applied to the classification of some…

We study smooth higher symmetry groups and moduli $\infty$-stacks of generic higher geometric structures on manifolds. Symmetries are automorphisms which cover non-trivial diffeomorphisms of the base manifold. We construct the smooth higher…

We define and study coisotropic structures on morphisms of commutative dg algebras in the context of shifted Poisson geometry, i.e. $P_n$-algebras. Roughly speaking, a coisotropic morphism is given by a $P_{n+1}$-algebra acting on a…

We study some interesting hypersurfaces that naturally arise when studying the period map on the moduli space of hypersurfaces, in the context of Sung Gi Park's recent work on studying the GIT moduli space of hypersurfaces via the minimal…

In this paper we complete the classification of topological symmetry groups for complete graphs $K_n$ by characterizing which $K_n$ can have a cyclic group, a dihedral group, or a subgroup of $D_m \times D_m$ where $m$ is odd, as its…

In this paper we analyze the structure of some subalgebras of quantized enveloping algebras corresponding to unipotent and solvable subgroups of a simple Lie group G. These algebras have the non--commutative structure of iterated algebras…

Let $\mathfrak g$ be a finite-dimensional Lie algebra. The symmetric algebra $\mathcal S(\mathfrak g)$ is equipped with the standard Lie-Poisson bracket. In this paper, we elaborate on a surprising observation that one naturally associates…

We construct families of quilted surfaces parametrized by the multiplihedra, and define moduli spaces of pseudoholomorphic quilted disks using the theory of pseudoholomorphic quilts of Wehrheim and Woodward. We prove a gluing theorem for…

These notes are an introduction to symplectic groupoids and the double structures associated with them. The treatment is intended to lie about midway between the original account of Coste, Dazord and Weinstein, which relied on effective use…

Let g be a complex, simple Lie algebra and t a Cartan subalgebra of g. A new unitary, flat connection on t with values in any finite-dimensional g-module V and simple poles along the root hyperplanes was recently introduced by J. Millson…

We describe a new sequence of polytopes which characterize A_infinity maps from a topological monoid to an A_infinity space. Therefore each of these polytopes is a quotient of the corresponding multiplihedron. Later term(s) in our sequence…

We study the noncommutative geometry of algebras of Lipschitz continuous and H\"older continuous functions where non-classical and novel differential geometric invariants arise. Indeed, we introduce a new class of Hochschild and cyclic…

We show that Khovanov homology and Hochschild homology theories share common structure. In fact they overlap: Khovanov homology of a $(2,n)$-torus link can be interpreted as a Hochschild homology of the algebra underlining the Khovanov…