Geodesic
PRIME SPECTRA OF AMBISKEW POLYNOMIAL RINGS
Glasgow mathematical journal, Tome 61 (2019) no. 1, pp. 49-68

Voir la notice de l'article provenant de la source Cambridge University Press

We determine sufficient criteria for the prime spectrum of an ambiskew polynomial algebra R over an algebraically closed field K to be akin to those of two of the principal examples of such an algebra, namely the universal enveloping algebra U(sl2) (in characteristic 0) and its quantization Uq(sl2) (when q is not a root of unity). More precisely, we determine sufficient criteria for the prime spectrum of R to consist of 0, the ideals (z − λ)R for some central element z of R and all λ ∈ K, and, for some positive integer d and each positive integer m, d height two prime ideals P for which R/P has Goldie rank m. 
FISH, CHRISTOPHER D.; JORDAN, DAVID A. PRIME SPECTRA OF AMBISKEW POLYNOMIAL RINGS. Glasgow mathematical journal, Tome 61 (2019) no. 1, pp. 49-68. doi: 10.1017/S0017089518000046
@article{10_1017_S0017089518000046,
     author = {FISH, CHRISTOPHER D. and JORDAN, DAVID A.},
     title = {PRIME {SPECTRA} {OF} {AMBISKEW} {POLYNOMIAL} {RINGS}},
     journal = {Glasgow mathematical journal},
     pages = {49--68},
     year = {2019},
     volume = {61},
     number = {1},
     doi = {10.1017/S0017089518000046},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089518000046/}
}
TY  - JOUR
AU  - FISH, CHRISTOPHER D.
AU  - JORDAN, DAVID A.
TI  - PRIME SPECTRA OF AMBISKEW POLYNOMIAL RINGS
JO  - Glasgow mathematical journal
PY  - 2019
SP  - 49
EP  - 68
VL  - 61
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S0017089518000046/
DO  - 10.1017/S0017089518000046
ID  - 10_1017_S0017089518000046
ER  - 
%0 Journal Article
%A FISH, CHRISTOPHER D.
%A JORDAN, DAVID A.
%T PRIME SPECTRA OF AMBISKEW POLYNOMIAL RINGS
%J Glasgow mathematical journal
%D 2019
%P 49-68
%V 61
%N 1
%U http://geodesic.mathdoc.fr/articles/10.1017/S0017089518000046/
%R 10.1017/S0017089518000046
%F 10_1017_S0017089518000046

[1] 1. Bavula, V. V., Generalized Weyl algebras and their representations, Algebra iAnal. 4 (3) (1992), 75–97; English transl. in St. Petersburg Math. J. (1993), 71–92. Google Scholar

[2] 2. Bavula, V. V., Filter dimension of algebras and modules, a simplicity criterion for generalized Weyl algebras, Commun. Algebra 24 (1996), 1971–1992. Google Scholar

[3] 3. Brown, K. A. and Goodearl, K. R., Lectures on algebraic quantum groups, Advanced courses in mathematics – CRM Barcelona (Birkhäuser, Basel, Boston, Berlin, 2002). Google Scholar

[4] 4. Chatters, A. W., Non-commutative unique factorization domains, Math. Proc. Camb. Philos. Soc. 95 (1) (1984), 49–54. Google Scholar

[5] 5. Dixmier, J., Enveloping algebras, Graduate studies in mathematics, vol. 11 (American Mathematical Society, Providence, RI, 1996). Google Scholar

[6] 6. Fish, C. D. and Jordan, D. A., Connected quantized Weyl algebras and quantum cluster algebras, J. Pure Appl. Algebra (2017), DOI:10.1016/j.jpaa2017.09.019. Google Scholar

[7] 7. Jordan, D. A., Iterated skew polynomial rings and quantum groups, J. Algebra 174 (1993), 267–281. Google Scholar

[8] 8. Jordan, D. A., Height one prime ideals of certain iterated skew polynomial rings, Math. Proc. Camb. Philos. Soc. 114 (1993), 407–425. Google Scholar

[9] 9. Jordan, D. A., Primitivity in skew Laurent polynomial rings and related rings, Math. Z. 213 (1993), 353–371. Google Scholar

[10] 10. Jordan, D. A., Down-up algebras and ambiskew polynomial rings, J. Algebra 228 (2000), 311–346. Google Scholar

[11] 11. Jordan, D. A. and Wells, I. E., Invariants for automorphisms of certain iterated skew polynomial rings, Proc. Edinb. Math. Soc. 39 (1996), 461–472. Google Scholar

[12] 12. Jordan, D. A. and Wells, I. E., Simple ambiskew polynomial rings, J. Algebra 382 (2013), 46–70. Google Scholar

[13] 13. Mcconnell, J. C. and Pettit, J. J., Crossed products and multiplicative analogues of Weyl algebras, J. Lond. Math. Soc. 38 (2) (1988), 47–55. Google Scholar

[14] 14. Mcconnell, J. C. and Robson, J. C., Noncommutative noetherian rings, (Wiley, Chichester, 1987). Google Scholar

[15] 15. Smith, S. P., A class of algebras similar to the enveloping algebra of sl(2, ℂ), Trans. Amer. Math. Soc. 322 (1990), 285–314. Google Scholar

[16] 16. Terwilliger, P. and Worawannotai, C., Augmented down-up algebras and uniform posets, Ars Math. Contemp. 6 (2) (2013), 409–417. Google Scholar

Cité par Sources :