Central extensions of three dimensional Artin-Schelter regular algebras

Fat point modules over generalized Laurent polynomial rings

“…Let Γ ⊂ P(V ) × P(V ) be the scheme defined by the zero locus of I 2 . If Γ is finite, then it follows from [6,Theorem 4.1.3] that Γ is the graph of a scheme automorphism τ : E → E. Furthermore the scheme E parametrizes the point modules of A, e.g., [6,Theorem 4.1.1]. A point module for a graded algebra is a graded, cyclic module which is generated in degree zero and has Hilbert series 1 1−t .…”

Double extension regular algebras of type (14641)

“…There has been extensive research on Artin-Schelter regular algebras of global dimension four; and many families of regular algebras have been discovered in recent years [8,10,[15][16][17][19][20][21][22][23]. The main goal of this paper is to construct and study a large class of new Artin-Schelter regular algebras of dimension four, called double Ore extensions.…”

Quasi-Lie structure of σ-derivations of C[t±1]

“…QuasiLie algebras include color Lie algebras, and in particular Lie algebras and Lie superalgebras, as well as various interesting quantum deformations of Lie algebras. Let us mention here as significant examples deformations of the Heisenberg Lie algebra, oscillator algebras, sl 2 and of other finite-dimensional Lie algebras, of infinite-dimensional Lie algebras of Witt and Virasoro type applied in physics within the string theory, vertex operator models, quantum scattering, lattice models and other contexts, as well as various algebras arising in connection to non-commutative geometry (see [3][4][5][6][7][8][9][10][11][12][13][14][16][17][18][19][20][21][26][27][28][29]34] and references therein). Many of these quantum deformations of Lie algebras can be shown to play the role of underlying algebraic objects for calculi of twisted, discretized or deformed derivations and difference type operators and thus in corresponding general non-commutative differential calculi.…”