Let G be a simple complex Lie group, g be its Lie algebra, K be a maximal compact form of G and k be a Lie algebra of K. We denote by X → X the anti-involution of g which singles out the compact form k. Consider the space of flat g-valued connections on a Riemann sphere with three holes which satisfy the additional condition A(z) = −A(z). We call the quotient of this space over the action of th...

We introduce Lie-Nijenhuis bialgebroids as Lie endowed with an additional derivation-like object. They give a complete infinitesimal description of Poisson-Nijenhuis groupoids, and key examples include manifolds, holomorphic flat bialgebra bundles. To achieve our goal we develop theory "generalized derivations" their duality, extending the well-established derivations on vector

Classical Lie Algebra Weight Systems of Arrow Diagrams Louis Leung Doctor of Philosophy Graduate Department of Mathematics University of Toronto 2010 The notion of finite type invariants of virtual knots introduced in [GPV] leads to the study of ~ An, the space of diagrams with n directed chords mod 6T (also known as the space of arrow diagrams), and weight systems on it. It is well known that ...

The present paper, though inspired by the use of tensor hierarchies in theoretical physics, establishes their mathematical credentials, especially as genetically related to Lie algebra crossed modules. Gauging procedures supergravity rely on a pairing – embedding between Leibniz and algebra. Two such algebras, together with tensor, form triple called Lie-Leibniz triple, which modules are partic...

We prove nilpotency results for Lie algebras over an arbitrary field admitting a derivation, which satisfies given polynomial identity r(t) = 0. In the special case of r=tn−1 we obtain uniform bound on class periodic derivation order n. even find optimal in characteristic p if does not divide certain invariant ρn.

In this paper we study the Lie algebras of derivations two-step nilpotent algebras. We obtain a class with trivial center and abelian ideal inner derivations. Among these, relations between complex real case indecomposable Heisenberg Leibniz are thoroughly described. Finally show that every almost derivation algebra one-dimensional commutator ideal, three exceptions, is an derivation.

We prove that the automorphisms of the generalized Witt Lie algebras W(m , n) over arbitrary commutative rings of characteristic p > 3 all come from automorphisms of the algebras on which they are defined as derivations. By descent theory, this result then implies that if a Lie algebra over a field becomes isomorphic to W{m, n) over the algebraic closure, it is a derivation algebra of the type ...

Let H be an infinite--dimensional Hilbert space and K(H) be the set of all compact operators on H. We will adopt spectral theorem for compact self-adjoint operators, to investigate of higher derivation and higher Jordan derivation on K(H) associated with the following cauchy-Jencen type functional equation 2f(frac{T+S}{2}+R)=f(T)+f(S)+2f(R) for all T,S,Rin K(H).

Let H be an innite dimensional Hilbert space and K(H) be the set of all compactoperators on H. We will adopt spectral theorem for compact self-adjoint operators, to investigate ofhigher derivation and higher Jordan derivation on K(H) associated with the following Cauchy-Jensentype functional equation 2f((T + S)/2+ R) = f(T ) + f(S) + 2f(R) for all T, S, R are in K(...