Biderivations of finite-dimensional complex simple Lie algebras
نویسندگان
چکیده
منابع مشابه
On permutably complemented subalgebras of finite dimensional Lie algebras
Let $L$ be a finite-dimensional Lie algebra. We say a subalgebra $H$ of $L$ is permutably complemented in $L$ if there is a subalgebra $K$ of $L$ such that $L=H+K$ and $Hcap K=0$. Also, if every subalgebra of $L$ is permutably complemented in $L$, then $L$ is called completely factorisable. In this article, we consider the influence of these concepts on the structure of a Lie algebra, in partic...
متن کاملClassification of finite dimensional simple Lie algebras in prime characteristics
We give a comprehensive survey of the theory of finite dimensional Lie algebras over an algebraically closed field of prime characteristic and announce that the classification of all finite dimensional simple Lie algebras over an algebraically closed field of characteristic p > 3 is now complete. Any such Lie algebra is up to isomorphism either classical or a filtered Lie algebra of Cartan type...
متن کاملQuantum Dynamical coBoundary Equation for finite dimensional simple Lie algebras
For a finite dimensional simple Lie algebra g, the standard universal solution R(x) ∈ Uq(g) ⊗2 of the Quantum Dynamical Yang–Baxter Equation quantizes the standard trigonometric solution of the Classical Dynamical Yang–Baxter Equation. It can be built from the standard R–matrix and from the solution F (x) ∈ Uq(g) ⊗2 of the Quantum Dynamical coCycle Equation as R(x) = F 21 (x)R F12(x). F (x) can...
متن کاملClassification of Finite-dimensional Semisimple Lie Algebras
Every finite-dimensional Lie algebra is a semi-direct product of a solvable Lie algebra and a semisimple Lie algebra. Classifying the solvable Lie algebras is difficult, but the semisimple Lie algebras have a relatively easy classification. We discuss in some detail how the representation theory of the particular Lie algebra sl2 tightly controls the structure of general semisimple Lie algebras,...
متن کاملOn 1-dimensional Representations of Finite W -algebras Associated to Simple Lie Algebras of Exceptional Type
We consider the finite W -algebra U(g, e) associated to a nilpotent element e ∈ g in a simple complex Lie algebra g of exceptional type. Using presentations obtained through an algorithm based on the PBW-theorem, we verify a conjecture of Premet, that U(g, e) always has a 1-dimensional representation, when g is of type G2, F4, E6 or E7. Thanks to a theorem of Premet, this allows one to deduce t...
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: Linear and Multilinear Algebra
سال: 2017
ISSN: 0308-1087,1563-5139
DOI: 10.1080/03081087.2017.1295433