A Graphic Demonstration of Insulin Dosage

Finite -algebras and intermediate statistics

“…One recognizes also the "deformed" gℓ(2) algebra, already considered in [3,4]. Two remarks need to be added.…”

Finite W-algebras and intermediate statistics

“…with G −,+,0 generated by {u, v, w}, {U, V, W } and {C s , C d , L, M} respectively. This grading is itself related to the sℓ(2, R) embedding obtained by taking the diagonal part of the sℓ(2, R)⊕sℓ(2, R) subalgebra of sp(4) [3,9]. Note that the sℓ(2, R) 2 negative root generator J − can be seen on the matrix (3.18) by selecting the G − part, that is by replacing by zero all the entries except the ones where stand J u , J v , and J w .…”

“…of a commutation relation (see below). As remarked in [3], this algebra has already been considered by P.W. Higgs as an algebra of conserved quantities for a Coulombic central force problem in a space of constant curvature [4].…”

“…Although many points still need to be clarified for a generalization of the anyon notion, one remarks that in the two cases considered above, the physical interpretation is brought by a finite W-algebra. In the one dimensional case, it is just the sℓ(2, R) Casimir operator, while in the two-dimensional one, it is exactly the finite W-algebra already described in [3] and [4]. Reconsidering the problem in the W-algebra framework can help a lot for setting more rapidly and systematically the algebraic formalism used in [5].…”