arXiv subjects

Wanchalerm Sucpikarnon

Publications and source records attributed to Wanchalerm Sucpikarnon.

3 recordsLinked to original sources

arXiv2024

Isometric Spectral Subtriples

We investigate the notion of subsystem in the framework of spectral triple as a generalized notion of noncommutative submanifold. In the case of manifolds, we consider several conditions on Dirac operators which turn embedded submanifolds into isometric submanifolds. We then suggest a definition of spectral subtriple based on the notion of submanifold algebra and the already existing notions of Riemannian, isometric, and totally geodesic morphisms. We have shown that our definitions work at least in some relevant almost commutative examples.

math-ph↗

arXiv2019

Classification of tensor decompositions for II$_1$ factors

In the mid thirties Murray and von Neumann found a natural way to associate a von Neumann algebra $L(Γ)$ to any countable discrete group $Γ$. Classifying $L(Γ)$ in term of $Γ$ is a notoriously complex problem as in general the initial data tends to be lost in the von Neumann algebraic regime. An important problem in the theory of von Neumann algebras is to completely describe all possible tensor decompositions of a given group von Neumann algebra $L(Γ)$. In this direction the main goal is to investigate how exactly a tensor decomposition of $L(Γ)$ relates to the underlying group $Γ$. In this dissertation we introduce several new classes of groups $Γ$ for which all tensor decompositions of $L(Γ)$ are parametrized by the canonical direct product decompositions of $Γ$. Specifically, we show that whenever $L(Γ)\cong M_1\bar\otimes M_2$ where $M_i$ are any diffuse von Neumann algebras then there exists a non-canonical direct product decomposition $Γ=Γ_1\timesΓ_2$ such that up to amplifications we have that $M_1\cong L(Γ_1)$ and $M_2\cong L(Γ_2)$. Our class include large classes of icc (infinite conjugacy class) amalgamated free products and wreath product groups. In addition we obtain similar classifications of tensor decompositions for the von Neumann algebras associated with the $T_0$ and $T_1$ group functors introduced by McDuff in $1969$.

math.OA↗

arXiv2017

Tensor product decompositions of II$_1$ factors arising from extensions of amalgamated free product groups

In this paper we introduce a new family of icc groups $Γ$ which satisfy the following product rigidity phenomenon, discovered in [DHI16] (see also [dSP17]): all tensor product decompositions of the II$_1$ factor $L(Γ)$ arise only from the canonical direct product decompositions of the underlying group $Γ$. Our groups are assembled from certain HNN-extensions and amalgamated free products and include many remarkable groups studied throughout mathematics such as graph product groups, poly-amalgam groups, Burger-Mozes groups, Higman group, various integral two-dimensional Cremona groups, etc. As a consequence, we obtain several new examples of groups that give rise to prime factors.

math.OA↗