Non-associative Frobenius algebras for simply laced Chevalley groups
نویسندگان
چکیده
We provide an explicit construction for a class of commutative, non-associative algebras each the simple Chevalley groups simply laced type. Moreover, we equip these with associating bilinear form, which turns them into Frobenius algebras. This includes 3876-dimensional algebra on group type E8 acts by automorphisms. also prove that admit structure (axial) decomposition
منابع مشابه
Non-simply-laced Clusters of Finite Type via Frobenius Morphism
By showing the compatibility of folding almost positive roots and folding cluster categories, we prove that there is a one-to-one correspondence between seeds and tilting seeds in non-simply-laced finite cases.
متن کاملColour valued scattering matrices from non simply-laced Lie algebras
A new set of exact scattering matrices in 1+1 dimensions is proposed by solving the bootstrap equations. Extending earlier constructions of colour valued scattering matrices this new set has its colour structure associated to non simply-laced Lie algebras. This in particular leads to a coupling of different affine Toda models whose fusing structure has to be matched in a suitable manner. The de...
متن کاملFrobenius Categories of Chevalley Groups
Notes for a course, held in the Biebrza Marshes, Poland, May 6–10, 2010, on Frobenius categories of finite groups of Lie type.
متن کاملAn approach to non simply laced cluster algebras
We study cluster algebras associated to a quiver equipped with a group of admissible automorphisms. This enables us to realize cluster algebras of non simply laced types as quotients of cluster algebras of simply laced types. We then generalize well known results on cluster algebras as denominators theorems and, under some conditions, the linear independence of cluster monomials over Z.
متن کاملDuality for nonlinear simply laced groups
We establish a character multiplicity duality for a certain natural class of nonlinear (nonalgebraic) groups arising as two-fold covers of simply laced real reductive algebraic groups. This allows us to extend part of the formalism of the Local Langlands Conjecture to such groups.
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: Transactions of the American Mathematical Society
سال: 2021
ISSN: ['2330-0000']
DOI: https://doi.org/10.1090/tran/8484