Tilting modules for the Auslander algebra of K[x]/(xn)

نویسندگان

چکیده

We construct an isomorphism between the partially ordered set of tilting modules for Auslander algebra K[x]/(xn) and interval rational permutation braids in braid group on n strands. Hence, there are only finitely many modules.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Cluster Tilting for Higher Auslander Algebras

The concept of cluster tilting gives a higher analogue of classical Auslander correspondence between representation-finite algebras and Auslander algebras. The n-Auslander-Reiten translation functor τn plays an important role in the study of n-cluster tilting subcategories. We study the category Mn of preinjective-like modules obtained by applying τn to injective modules repeatedly. We call a f...

متن کامل

Rigidity of Tilting Modules

Let Uq denote the quantum group associated with a finite dimensional semisimple Lie algebra. Assume that q is a complex root of unity of odd order and that Uq is obtained via Lusztig’s q-divided powers construction. We prove that all regular projective (tilting) modules for Uq are rigid, i.e., have identical radical and socle filtrations. Moreover, we obtain the same for a large class of Weyl m...

متن کامل

Algebraic Modules and the Auslander–Reiten Quiver

Recall that an algebraic module is aKG-module that satisfies a polynomial with integer coefficients, with addition and multiplication given by direct sum and tensor product. In this article we prove that non-periodic algebraic modules are very rare, and that if the complexity of an algebraic module is at least 3, then it is the only algebraic module on its component of the (stable) Auslander–Re...

متن کامل

Constructing Tilting Modules

We investigate the structure of (infinite dimensional) tilting modules over hereditary artin algebras. For connected algebras of infinite representation type with Grothendieck group of rank n, we prove that for each 0 ≤ i < n− 1, there is an infinite dimensional tilting module Ti with exactly i pairwise non-isomorphic indecomposable finite dimensional direct summands. We also show that any ston...

متن کامل

The Auslander-reiten Formula for Complexes of Modules

An Auslander-Reiten formula for complexes of modules is presented. This formula contains as a special case the classical Auslander Reiten formula. The AuslanderReiten translate of a complex is described explicitly, and various applications are discussed.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Communications in Algebra

سال: 2021

ISSN: ['1532-4125', '0092-7872']

DOI: https://doi.org/10.1080/00927872.2021.1951748