BGG-resolution for α-stratified modules over simply-laced finite-dimensional Lie algebras
نویسندگان
چکیده
منابع مشابه
A 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 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 کاملOn Simply Laced Lie Algebras and Their Minuscule Representations
The Lie algebra E6 may be defined as the algebra of endomorphisms of a 27-dimensional complex vector space MC which annihilate a particular cubic polynomial. This raises a natural question: what is this polynomial? If we choose a basis for MC consisting of weight vectors {Xw} (for some Cartan subalgebra of E6), then any invariant cubic polynomial must be a linear combination of monomials XwXw′X...
متن کاملConstructing Simply Laced Lie Algebras from Extremal Elements
For any finite graph Γ and any field K of characteristic unequal to 2 we construct an algebraic variety X over K whose K-points parameterise K-Lie algebras generated by extremal elements, corresponding to the vertices of the graph, with prescribed commutation relations, corresponding to the non-edges. After that, we study the case where Γ is a connected, simply laced Dynkin diagram of finite or...
متن کاملKoszul Duality for Modules over Lie Algebras
Let g be a reductive Lie algebra over a field of characteristic zero. Suppose that g acts on a complex of vector spaces M by iλ and Lλ, which satisfy the same identities that contraction and Lie derivative do for differential forms. Out of this data one defines the cohomology of the invariants and the equivariant cohomology of M. We establish Koszul duality between them.
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: Kyoto Journal of Mathematics
سال: 1998
ISSN: 2156-2261
DOI: 10.1215/kjm/1250518115