Current algebras and categorified quantum groups
نویسندگان
چکیده
منابع مشابه
Higher Categorified Algebras versus Bounded Homotopy Algebras
We define Lie 3-algebras and prove that these are in 1-to-1 correspondence with the 3-term Lie infinity algebras whose bilinear and trilinear maps vanish in degree (1, 1) and in total degree 1, respectively. Further, we give an answer to a question of [Roy07] pertaining to the use of the nerve and normalization functors in the study of the relationship between categorified algebras and truncate...
متن کاملCategorified Algebra and Quantum Mechanics
The process some call ‘categorification’ consists of interpreting set-theoretic structures in mathematics as derived from category-theoretic structures. Examples include the interpretation of as the Burnside rig of the category of finite sets with product and coproduct, and of [x] in terms the category of combinatorial species. This has interesting applications to quantum mechanics, and in part...
متن کاملGeneralized quantum current algebras
Two general families of new quantum deformed current algebras are proposed and identified both as infinite Hopf family of algebras, a structure which enable one to define “tensor products” of these algebras. The standard quantum affine algebras turn out to be a very special case of both algebra families, in which case the infinite Hopf family structure degenerates into standard Hopf algebras. T...
متن کاملquantum groups and double quiver algebras
Let Uq(g) be the Drinfeld-Jimbo quantum group, which is a deformation of the universal enveloping algebra of a finite dimensional semisimple Lie algebra g. In the generic case, i.e. the parameter q is not a root of unity, several models have been raised to realize it. For example, the Ringel-Hall algebra approach is one successful model among them, see [10, 5, 11]. The case where q is a root of...
متن کاملQuantum Groups and Fuss-catalan Algebras
The categories of representations of compact quantum groups of automorphisms of certain inclusions of finite dimensional C∗-algebras are shown to be isomorphic to the categories of Fuss-Catalan diagrams. A Fuss-Catalan diagram is a planar diagram formed by an upper row of 4m points, a lower row of 4n points and by 2m+2n non-crossing strings joining them. Both rows of points are colored from lef...
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 the London Mathematical Society
سال: 2017
ISSN: 0024-6107,1469-7750
DOI: 10.1112/jlms.12001