Let be a semisimple complex algebraic group and its flag variety. Let and let be its enveloping algebra. Let be a Cartan subalgebra of . For , let be the corresponding minimal primitive ideal, let , and let be the Hattori-Stallings trace. Results of Hodges suggest to study this map as a step towards a classification, up to isomorphism or Morita equivalence, of the -algebras . When is regular, Hodges has shown that . In this case is generated by the classes corresponding to -linearized line bundles on , and the value of on these generators was computed by Hodges and Holland, in a special case, and then by Perets and the author, in general. This result is extended here to the singular case.
Soient un groupe algébrique semi-simple complexe, , l’algèbre enveloppante de , et la variété des drapeaux de . Soit une sous-algèbre de Cartan de . Pour , soit l’idéal primitif minimal correspondant, soit , et la trace de Hattori-Stallings. Des résultats de Hodges suggèrent d’étudier cette application en vue de classifier les -algèbres à isomorphisme ou équivalence de Morita près. Pour régulier, Hodges a montré que . Dans ce cas, est engendré par les classes correspondant aux fibrés en droites -linéarisés sur , et la valeur de sur ces générateurs a été calculée par Hodges et Holland, dans un cas particulier, puis par Perets et l’auteur en général. Nous étendons ici ce résultat au cas singulier.
@article{AIF_1995__45_3_707_0, author = {Polo, Patrick}, title = {On the $K$-theory and {Hattori-Stallings} traces of minimal primitive factors of enveloping algebras of semisimple {Lie} algebras : the singular case}, journal = {Annales de l'Institut Fourier}, pages = {707--720}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {45}, number = {3}, year = {1995}, doi = {10.5802/aif.1471}, zbl = {0818.17006}, mrnumber = {96i:17006}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1471/} }
TY - JOUR AU - Polo, Patrick TI - On the $K$-theory and Hattori-Stallings traces of minimal primitive factors of enveloping algebras of semisimple Lie algebras : the singular case JO - Annales de l'Institut Fourier PY - 1995 SP - 707 EP - 720 VL - 45 IS - 3 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.1471/ DO - 10.5802/aif.1471 LA - en ID - AIF_1995__45_3_707_0 ER -
%0 Journal Article %A Polo, Patrick %T On the $K$-theory and Hattori-Stallings traces of minimal primitive factors of enveloping algebras of semisimple Lie algebras : the singular case %J Annales de l'Institut Fourier %D 1995 %P 707-720 %V 45 %N 3 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.1471/ %R 10.5802/aif.1471 %G en %F AIF_1995__45_3_707_0
Polo, Patrick. On the $K$-theory and Hattori-Stallings traces of minimal primitive factors of enveloping algebras of semisimple Lie algebras : the singular case. Annales de l'Institut Fourier, Volume 45 (1995) no. 3, pp. 707-720. doi : 10.5802/aif.1471. https://aif.centre-mersenne.org/articles/10.5802/aif.1471/
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