ترغب بنشر مسار تعليمي؟ اضغط هنا

Realization of rigid C*-bicategories as bimodules over type II$_1$ von Neumann algebras

80   0   0.0 ( 0 )
 نشر من قبل Luca Giorgetti
 تاريخ النشر 2020
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

We prove that every rigid C*-bicategory with finite-dimensional centers (finitely decomposable horizontal units) can be realized as Connes bimodules over finite direct sums of II$_1$ factors. In particular, we realize every multitensor C*-category as bimodules over a finite direct sum of II$_1$ factors.



قيم البحث

اقرأ أيضاً

We discuss the structure of the Motzkin algebra $M_k(D)$ by introducing a sequence of idempotents and the basic construction. We show that $cup_{kgeq 1}M_k(D)$ admits a factor trace if and only if $Din {2cos(pi/n)+1|ngeq 3}cup [3,infty)$ and higher c ommutants of these factors depend on $D$. Then a family of irreducible bimodules over the factors are constructed. A tensor category with $A_n$ fusion rule is obtained from these bimodules.
We study differential operators on complete Riemannian manifolds which act on sections of a bundle of finite type modules over a von Neumann algebra with a trace. We prove a relative index and a Callias-type index theorems for von Neumann indexes of such operators. We apply these results to obtain a version of Atiyahs $L^2$-index theorem, which states that the index of a Callias-type operator on a non-compact manifold $M$ is equal to the $Gamma$-index of its lift to a Galois cover of $M$. We also prove the cobordism invariance of the index of Callias-type operators. In particular, we give a new proof of the cobordism invariance of the von Neumann index of operators on compact manifolds.
169 - Pere Ara , Joan Claramunt 2017
For a division ring $D$, denote by $mathcal M_D$ the $D$-ring obtained as the completion of the direct limit $varinjlim_n M_{2^n}(D)$ with respect to the metric induced by its unique rank function. We prove that, for any ultramatricial $D$-ring $math cal B$ and any non-discrete extremal pseudo-rank function $N$ on $mathcal B$, there is an isomorphism of $D$-rings $overline{mathcal B} cong mathcal M_D$, where $overline{mathcal B}$ stands for the completion of $mathcal B$ with respect to the pseudo-metric induced by $N$. This generalizes a result of von Neumann. We also show a corresponding uniqueness result for $*$-algebras over fields $F$ with positive definite involution, where the algebra $mathcal M_F$ is endowed with its natural involution coming from the $*$-transpose involution on each of the factors $M_{2^n}(F)$.
125 - Matteo Tommasini 2014
We fix any bicategory $mathscr{A}$ together with a class of morphisms $mathbf{W}_{mathscr{A}}$, such that there is a bicategory of fractions $mathscr{A}[mathbf{W}_{mathscr{A}}^{-1}]$. Given another such pair $(mathscr{B},mathbf{W}_{mathscr{B}})$ and any pseudofunctor $mathcal{F}:mathscr{A}rightarrowmathscr{B}$, we find necessary and sufficient conditions in order to have an induced pseudofunctor $mathcal{G}:mathscr{A}[mathbf{W}_{mathscr{A}}^{-1}]rightarrow mathscr{B}[mathbf{W}_{mathscr{B}}^{-1}]$. Moreover, we give a simple description of $mathcal{G}$ in the case when the class $mathbf{W}_{mathscr{B}}$ is right saturated.
279 - Lu Cui , Linzhe Huang , Wenming Wu 2021
A unital ring is called clean (resp. strongly clean) if every element can be written as the sum of an invertible element and an idempotent (resp. an invertible element and an idempotent that commutes). T.Y. Lam proposed a question: which von Neumann algebras are clean as rings? In this paper, we characterize strongly clean von Neumann algebras and prove that all finite von Neumann algebras and all separable infinite factors are clean.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا