Triangular Decomposition of Tame Non-Simply Laced Composition Algebras
نویسندگان
چکیده
منابع مشابه
Colour 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 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 کاملBmw Algebras of Simply Laced Type
It is known that the recently discovered representations of the Artin groups of type An, the braid groups, can be constructed via BMW algebras. We introduce similar algebras of type Dn and En which also lead to the newly found faithful representations of the Artin groups of the corresponding types. We establish finite dimensionality of these algebras. Moreover, they have ideals I1 and I2 with I...
متن کاملBrauer Algebras of Simply Laced Type
The diagram algebra introduced by Brauer that describes the centralizer algebra of the n-fold tensor product of the natural representation of an orthogonal Lie group has a presentation by generators and relations that only depends on the path graph An−1 on n− 1 nodes. Here we describe an algebra depending on an arbitrary graph M , called the Brauer algebra of type M , and study its structure in...
متن کاملA Combinatorial Construction for Simply–laced Lie Algebras
This paper shows how to uniformly associate Lie algebras to the simply-laced Dynkin diagrams excluding E8 by constructing explicit combinatorial models of minuscule representations using only graph-theoretic ideas. This involves defining raising and lowering operators in a space of ideals of certain distributive lattices associated to sequences of vertices of the Dynkin diagram.
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 Algebra
سال: 2001
ISSN: 0021-8693
DOI: 10.1006/jabr.2001.8770