Singular

7.5.10 ncalg_lib

Library:

ncalg.lib

Purpose:

Definitions of important G- and GR-algebras

Authors:

Viktor Levandovskyy, [email protected],
Oleksandr Motsak, U@D, where U={motsak}, D={mathematik.uni-kl.de}

Conventions:

This library provides pre-defined important noncommutative algebras.
For universal enveloping algebras of finite dimensional Lie algebras sl_n, gl_n, g_2 etc. there are functions makeUsl, makeUgl, makeUg2 etc.
For quantized enveloping algebras U_q(sl_2) and U_q(sl_3), there are functions makeQsl2, makeQsl3) and for non-standard quantum deformation of so_3, there is the function makeQso3.
For bigger algebras we suppress the output of the (lengthy) list of non-commutative relations and provide only the number of these relations instead.

Procedures:

7.5.10.0. makeUsl2		create U(sl_2) in the variables (e,f,h) in char p>=0
7.5.10.0. makeUsl		create U(sl_n) in char p>=0
7.5.10.0. makeUgl		create U(gl_n) in the variables (e_i_j (1<i,j<n)) in char p>=0
7.5.10.0. makeUso5		create U(so_5) in the variables (x(i),y(i),H(i)) in char p>=0
7.5.10.0. makeUso6		create U(so_6) in the variables (x(i),y(i),H(i)) in char p>=0
7.5.10.0. makeUso7		create U(so_7) in the variables (x(i),y(i),H(i)) in char p>=0
7.5.10.0. makeUso8		create U(so_8) in the variables (x(i),y(i),H(i)) in char p>=0
7.5.10.0. makeUso9		create U(so_9) in the variables (x(i),y(i),H(i)) in char p>=0
7.5.10.0. makeUso10		create U(so_{10}) in the variables (x(i),y(i),H(i)) in char p>=0
7.5.10.0. makeUso11		create U(so_{11}) in the variables (x(i),y(i),H(i)) in char p>=0
7.5.10.0. makeUso12		create U(so_{12}) in the variables (x(i),y(i),H(i)) in char p>=0
7.5.10.0. makeUsp1		create U(sp_1) in the variables (x(i),y(i),H(i)) in char p>=0
7.5.10.0. makeUsp2		create U(sp_2) in the variables (x(i),y(i),H(i)) in char p>=0
7.5.10.0. makeUsp3		create U(sp_3) in the variables (x(i),y(i),H(i)) in char p>=0
7.5.10.0. makeUsp4		create U(sp_4) in the variables (x(i),y(i),H(i)) in char p>=0
7.5.10.0. makeUsp5		create U(sp_5) in the variables (x(i),y(i),H(i)) in char p>=0
7.5.10.0. makeUg2		create U(g_2) in the variables (x(i),y(i),Ha,Hb) in char p>=0
7.5.10.0. makeUf4		create U(f_4) in the variables (x(i),y(i),H(i)) in char p>=0
7.5.10.0. makeUe6		create U(e_6) in the variables (x(i),y(i),H(i)) in char p>=0
7.5.10.0. makeUe7		create U(e_7) in the variables (x(i),y(i),H(i)) in char p>=0
7.5.10.0. makeUe8		create U(e_8) in the variables (x(i),y(i),H(i)) in char p>=0
7.5.10.0. makeQso3		create U_q(so_3) in the presentation of Klimyk (if int n is given, the quantum parameter will be specialized at the 2n-th root of unity)
7.5.10.0. makeQsl2		preparation for U_q(sl_2) as factor-algebra; if n is specified, the quantum parameter q will be specialized at the n-th root of unity
7.5.10.0. makeQsl3		preparation for U_q(sl_3) as factor-algebra; if n is specified, the quantum parameter q will be specialized at the n-th root of unity
7.5.10.0. Qso3Casimir		returns a list with the (optionally normalized) Casimir elements of U_q(so_3) for the quantum parameter specialized at the 2n-th root of unity
7.5.10.0. GKZsystem		define a ring and a Gelfand-Kapranov-Zelevinsky system of differential equations