The Grothendieck group of a cluster category
نویسندگان
چکیده
منابع مشابه
THE GROTHENDIECK GROUP OF AN n-ANGULATED CATEGORY
We define the Grothendieck group of an n-angulated category and show that for odd n its properties are as in the special case of n = 3, i.e. the triangulated case. In particular, its subgroups classify the dense and complete n-angulated subcategories via a bijective correspondence. For a tensor n-angulated category, the Grothendieck group becomes a ring, whose ideals classify the dense and comp...
متن کاملThe Grothendieck Group
In the red corner, topological K-theory! The study of stable equivalences of vector bundles over a topological space, and the engine behind Bott periodicity, a result whose reverberations are felt throughout algebraic topology. In the blue corner, modular representation theory! The story of representations in positive characteristic, where the CDE triangle powers applications in group theory an...
متن کاملThe Grothendieck Group of Hopf Algebras
Let H be a cosemisimple Hopf algebra over an algebraically closed field k. Assume that H contains a simple subcoalgebra of dimension 9. We show that if H has no simple subcoalgebras of even dimension then H contains either a grouplike element with order 2 or 3, a Hopf subalgebra of dimension 75, or a family of simple subcoalgebras whose dimensions are the squares of each positive odd integer. I...
متن کاملOn a quantum analog of the Grothendieck-Teichmüller group
We introduce a self-dual, noncommutative, and noncocommutative Hopf algebra HGT which takes for certain Hopf categories (and therefore braided monoidal bicategories) a similar role as the GrothendieckTeichmüller group for quasitensor categories. We also give a result which highly restricts the possibility for similar structures for higher weak n-categories (n ≥ 3) by showing that these structur...
متن کاملThe Grothendieck Group of a Quantum Projective Space Bundle
We compute the Grothendieck group K0 of non-commutative analogues of projective space bundles. Our results specialize to give the K0-groups of non-commutative analogues of projective spaces, and specialize to recover the K0-group of a usual projective space bundle over a regular noetherian separated scheme. As an application, we develop an intersection theory for quantum ruled surfaces.
متن کاملذخیره 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: Journal of Pure and Applied Algebra
سال: 2008
ISSN: 0022-4049
DOI: 10.1016/j.jpaa.2007.04.007