اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدOn geometrically defined extensions of the Temperley-Lieb category in the Brauer category
262
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We define an infinite chain of subcategories of the partition category by introducing the left-height ($l$) of a partition. For the Brauer case, the chain starts with the Temperley-Lieb ($l=-1$) and ends with the Brauer ($l=infty$) category. The End sets are algebras, i.e., an infinite tower thereof for each $l$, whose representation theory is studied in the paper.
قيم البحث
اقرأ أيضاً
In this paper, we will study the Dieck-Temlerley-Lieb algebras of type Bn and Cn. We compute their ranks and describe a basis for them by using some results from corresponding Brauer algebras and Temperley-Lieb algebras.
We first give a short intrinsic, diagrammatic proof of the First Fundamental Theorem of invariant theory (FFT) for the special orthogonal group $text{SO}_m(mathbb{C})$, given the FFT for $text{O}_m(mathbb{C})$. We then define, by means of a presentat
ion with generators and relations, an enhanced Brauer category $widetilde{mathcal{B}}(m)$ by adding a single generator to the usual Brauer category $mathcal{B}(m)$, together with four relations. We prove that our category $widetilde{mathcal{B}}(m)$ is actually (and remarkably) {em equivalent} to the category of representations of $text{SO}_m$ generated by the natural representation. The FFT for $text{SO}_m$ amounts to the surjectivity of a certain functor $mathcal{F}$ on $text{Hom}$ spaces, while the Second Fundamental Theorem for $text{SO}_m$ says simply that $mathcal{F}$ is injective on $text{Hom}$ spaces. This theorem provides a diagrammatic means of computing the dimensions of spaces of homomorphisms between tensor modules for $text{SO}_m$ (for any $m$). These methods will be applied to the case of the orthosymplectic Lie algebras $text{osp}(m|2n)$, where the super-Pfaffian enters, in a future work.
A well-known theorem of Buchweitz provides equivalences between three categories: the stable category of Gorenstein projective modules over a Gorenstein algebra, the homotopy category of acyclic complexes of projectives, and the singularity category.
To adapt this result to $N$-complexes, one must find an appropriate candidate for the $N$-analogue of the stable category. We identify this $N$-stable category via the monomorphism category and prove Buchweitzs theorem for $N$-complexes over a Frobenius exact abelian category. We also compute the Serre functor on the $N$-stable category over a self-injective algebra and study the resultant fractional Calabi-Yau properties.
We introduce the category of finite strings and study its basic properties. The category is closely related to the augmented simplex category, and it models categories of linear representations. Each lattice of non-crossing partitions arises naturally as a lattice of subobjects.
We prove the twisted Whittaker category on the affine flag variety and the category of representations of the mixed quantum group are equivalent.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
