Geodesic
Dimension and enumeration of primitive ideals in quantum algebras
Journal of Algebraic Combinatorics, Tome 29 (2009) no. 3, pp. 269-294.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: In this paper, we study the primitive ideals of quantum algebras supporting a rational torus action. We first prove a quantum analogue of a Theorem of Dixmier; namely, we show that the Gelfand-Kirillov dimension of primitive factors of various quantum algebras is always even. Next we give a combinatorial criterion for a prime ideal that is invariant under the torus action to be primitive. We use this criterion to obtain a formula for the number of primitive ideals in the algebra of $2\times n$ quantum matrices that are invariant under the action of the torus. Roughly speaking, this can be thought of as giving an enumeration of the points that are invariant under the induced action of the torus in the "variety of $2\times n$ quantum matrices".
Keywords: keywords primitive ideals, quantum matrices, quantised enveloping algebras, cauchon diagrams, perfect matchings, pfaffians 
@article{JAC_2009__29_3_a5,
     author = {Bell, J. and Launois, S. and Nguyen, N.},
     title = {Dimension and enumeration of primitive ideals in quantum algebras},
     journal = {Journal of Algebraic Combinatorics},
     pages = {269--294},
     publisher = {mathdoc},
     volume = {29},
     number = {3},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_2009__29_3_a5/}
}
TY  - JOUR
AU  - Bell, J.
AU  - Launois, S.
AU  - Nguyen, N.
TI  - Dimension and enumeration of primitive ideals in quantum algebras
JO  - Journal of Algebraic Combinatorics
PY  - 2009
SP  - 269
EP  - 294
VL  - 29
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JAC_2009__29_3_a5/
LA  - en
ID  - JAC_2009__29_3_a5
ER  - 
%0 Journal Article
%A Bell, J.
%A Launois, S.
%A Nguyen, N.
%T Dimension and enumeration of primitive ideals in quantum algebras
%J Journal of Algebraic Combinatorics
%D 2009
%P 269-294
%V 29
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JAC_2009__29_3_a5/
%G en
%F JAC_2009__29_3_a5
Bell, J.; Launois, S.; Nguyen, N. Dimension and enumeration of primitive ideals in quantum algebras. Journal of Algebraic Combinatorics, Tome 29 (2009) no. 3, pp. 269-294. http://geodesic.mathdoc.fr/item/JAC_2009__29_3_a5/