Graded Lie algebra of Hermitian tangent valued forms

Tangent Lie algebra of derived Artin stacks

Since the work of Mikhail Kapranov in [Kap], it is known that the shifted tangent complex TX r ́1s of a smooth algebraic variety X is endowed with a weak Lie structure. Moreover any complex of quasi-coherent sheaves on X is endowed with a weak Lie action of this tangent Lie algebra. We will generalize this result to (finite enough) derived Artin stacks, without any smoothness assumption. This in...

Vector valued hermitian and quaternionic modular forms

Lie triple derivation algebra of Virasoro-like algebra

Let $mathfrak{L}$ be the Virasoro-like algebra and $mathfrak{g}$ itsderived algebra, respectively. We investigate the structure of the Lie triplederivation algebra of $mathfrak{L}$ and $mathfrak{g}$. We provethat they are both isomorphic to $mathfrak{L}$, which provides twoexamples of invariance under triple derivation.

Graded Contractions of Bilinear Invariant Forms of Lie Algebras

ABSTRACT. We introduce a new construction of bilinear invariant forms on Lie algebras, based on the method of graded contractions. The general method is described and the Z2-, Z3-, and Z2 ⊗ Z2-contractions are found. The results can be applied to all Lie algebras and superalgebras (finite or infinite dimensional) which admit the chosen gradings. We consider some examples: contractions of the Ki...

Small Zeros of Hermitian Forms over a Quaternion Algebra

Let D be a positive definite quaternion algebra over a totally real number field K, F (X, Y ) a hermitian form in 2N variables over D, and Z a right D-vector space which is isotropic with respect to F . We prove the existence of a small-height basis for Z over D, such that F (X, X) vanishes at each of the basis vectors. This constitutes a non-commutative analogue of a theorem of Vaaler [19], an...