In this paper we consider deformations of finite or infinite dimensional Lie algebras over a field of characteristic 0. By “deformations of a Lie algebra” we mean the (affine algebraic) manifold of… (More)

We show that if a Legendrian knot in standard contact R3 possesses a generating family then there exists an augmentation of the Chekanov-Eliashberg DGA so that the associated linearized contact… (More)

(Sometimes the generators of the Virasoro algebra are denoted by Li; to translate our results into these notations one should put ei = −L−i.) The Lie algebra Vir is graded, Vir = ⊕k∈Z Virk (deg ei =… (More)

We study projectively self-dual polygons and curves in the projective plane. Our results provide a partial answer to problem No 1994-17 in the book of Arnold’s problems (2004).

The Lie algebra W = Der A is called the Witt algebra. It consists of “vector fields” f∂, f ∈ A. In particular, dimF W = dimF A = p. As any Lie algebra of derivations of a commutative algebra over F,… (More)

BSG with constant composition (ca. 4.7 wt% B) was deposited using Tris(trimethylsiloxy) boron B[OSi(CH3)3] 3 in a standard LPCVD system. The optimum deposition conditions are 800 °C, 105 Pa (800… (More)

We prove an explicit formula for a projection of singular vectors in the Verma module over a rank 2 Kac–Moody Lie algebra onto the universal enveloping algebra of the Heisenberg Lie algebra and of… (More)