### 7.7.11 ncalg_lib

Library:
  ncalg.lib
Purpose:
  Definitions of important G- and GR-algebras
Authors:
  Viktor Levandovskyy, levandov@mathematik.uni-kl.de,
  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:

> 7.7.11.0. makeUsl2 |  | create U(sl_2) in the variables (e,f,h) in char p>=0
> 7.7.11.0. makeUsl |  | create U(sl_n) in char p>=0
> 7.7.11.0. makeUgl |  | create U(gl_n) in the variables (e_i_j (1<i,j<n)) in char p>=0
> 7.7.11.0. makeUso5 |  | create U(so_5) in the variables (x(i),y(i),H(i)) in char p>=0
> 7.7.11.0. makeUso6 |  | create U(so_6) in the variables (x(i),y(i),H(i)) in char p>=0
> 7.7.11.0. makeUso7 |  | create U(so_7) in the variables (x(i),y(i),H(i)) in char p>=0
> 7.7.11.0. makeUso8 |  | create U(so_8) in the variables (x(i),y(i),H(i)) in char p>=0
> 7.7.11.0. makeUso9 |  | create U(so_9) in the variables (x(i),y(i),H(i)) in char p>=0
> 7.7.11.0. makeUso10 |  | create U(so_{10}) in the variables (x(i),y(i),H(i)) in char p>=0
> 7.7.11.0. makeUso11 |  | create U(so_{11}) in the variables (x(i),y(i),H(i)) in char p>=0
> 7.7.11.0. makeUso12 |  | create U(so_{12}) in the variables (x(i),y(i),H(i)) in char p>=0
> 7.7.11.0. makeUsp1 |  | create U(sp_1) in the variables (x(i),y(i),H(i)) in char p>=0
> 7.7.11.0. makeUsp2 |  | create U(sp_2) in the variables (x(i),y(i),H(i)) in char p>=0
> 7.7.11.0. makeUsp3 |  | create U(sp_3) in the variables (x(i),y(i),H(i)) in char p>=0
> 7.7.11.0. makeUsp4 |  | create U(sp_4) in the variables (x(i),y(i),H(i)) in char p>=0
> 7.7.11.0. makeUsp5 |  | create U(sp_5) in the variables (x(i),y(i),H(i)) in char p>=0
> 7.7.11.0. makeUg2 |  | create U(g_2) in the variables (x(i),y(i),Ha,Hb) in char p>=0
> 7.7.11.0. makeUf4 |  | create U(f_4) in the variables (x(i),y(i),H(i)) in char p>=0
> 7.7.11.0. makeUe6 |  | create U(e_6) in the variables (x(i),y(i),H(i)) in char p>=0
> 7.7.11.0. makeUe7 |  | create U(e_7) in the variables (x(i),y(i),H(i)) in char p>=0
> 7.7.11.0. makeUe8 |  | create U(e_8) in the variables (x(i),y(i),H(i)) in char p>=0
> 7.7.11.0. 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)
> 7.7.11.0. 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
> 7.7.11.0. 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
> 7.7.11.0. 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
> 7.7.11.0. GKZsystem |  | define a ring and a Gelfand-Kapranov-Zelevinsky system of differential equations

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