We study finite-dimensional Lie algebras of polynomial vector fields in n variables that contain the vector fields âˆ‚ âˆ‚xi (i = 1, . . . , n) and x1 âˆ‚ âˆ‚x1 +Â· Â· Â·+xn âˆ‚ âˆ‚xn . We derive some generalâ€¦ (More)

Families of operator identities related to certain powers of positive root generators of (super) Lie algebras of first-order differential operators and q-deformed algebras of first-orderâ€¦ (More)

We study finite-dimensional Lie algebras L of polynomial vector fields in n variables that contain the vector fields âˆ‚ âˆ‚xi (i = 1, . . . , n) and x1 âˆ‚ âˆ‚x1 + Â· Â· Â· + xn âˆ‚ âˆ‚xn . We show that theâ€¦ (More)

NICO VAN DEN HIJLIGENBERG, YOURI KOTCHETKOV, G. Post

2010

For the Lie algebras L\(H(2)) and L\(W(2)), we study their infinitesimal deformations and the corresponding global ones. We show that, as in the case of L\{W(\)), each integrable infinitesimalâ€¦ (More)

This note is devoted to a more detailed description of one of the five simple exceptional Lie superalgebras of vector fields, cvect(0|3) * , a subalgebra of vect(4|3). We derive differentialâ€¦ (More)

We discuss a certain generalization of gl,,(C), and show how it is connected to polynomial differential operators that leave the polynomial space ~,~ invariant. Mathematics Subject Classificationsâ€¦ (More)

We consider the quantum hyperplane x ' x J = q , j x J x ' (i, j = 1..n) and define and consider = 'J and fl'J are complex numbers. We deformations of the form x ' x J q,~ x J x ~ + Zk ~ J X k +â€¦ (More)

Certain infinite families of operator identities related to powers of positive root generators of (super) Lie algebras of first-order differential operators and q-deformed algebras of first-orderâ€¦ (More)