Generalizations of Witt algebras over a field of characteristic zero

On the support of irreducible modules over the Witt–Kaplansky algebras of rank (2, 2)

“…Then there exists Aesupp V such that the pair a(A) and /3(A) is generating, linearly independent over Z and Proof. As is well known, © is simple (see for example [4]). Suppose that there do not exist a (A) and /3(A) which satisfy the conditions of the lemma.…”

“…In the present paper we propose the analogue of this theorem for another class of simple infinite-dimensional Lie algebras. These algebras appear as some generalization of the well-known Witt algebra in [3] and were studied in [8,9,4] (see also references therein). In particular, this class contains the algebra of derivations of C[x, ,x 2 ,xj ] , xj 1 ] which was studied in several papers during the last years (see for example [7] and references therein).…”

Generalized Heisenberg-Virasoro algebras

“…The following theorem is due to Kawamoto [10]. In this paper, we always suppose that ϕ is nondegenerate.…”

Weyl Type Algebras From Quantum Tori

“…Several different generalizations of Cartan type Lie algebras were given by Kawamoto [11], Osborn [18], Dokovic and Zhao [5][6][7], Osborn and Zhao [20,21], Xu [28,29], Passman [22], Bergen and Passman [2], Jordan [9], and others. In particular, Passman [22] and Jordan [9] constructed the Lie algebras AD = A ⊗ D of generalized Witt type from a unital commutative associative algebra A and a commutative algebra D of its derivations over a field F of arbitrary characteristic.…”