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JOURNALS // Moscow Mathematical Journal

Mosc. Math. J., 2021, Volume 21, Number 2, Pages 383–399 (Mi mmj797)

Goldie ranks of primitive ideals and indexes of equivariant Azumaya algebras
I. Losev, I. Panin

References

1. R. Bezrukavnikov and I. Losev, “On dimension growth of modular irreducible representations of semisimple Lie algebras”, Lie groups, geometry, and representation theory, Progr. Math., 326, Birkhäuser/Springer, Cham, 2018, 59–89  crossref  mathscinet  zmath
2. J. Brundan, “Mœglin's theorem and Goldie rank polynomials in Cartan type $A$”, Compos. Math., 147:6 (2011), 1741–1771  crossref  mathscinet  zmath
3. J. Brundan, S. M. Goodwin, and A. Kleshchev, “Highest weight theory for finite $W$-algebras”, Int. Math. Res. Not. IMRN, 2008, no. 15, rnn051, 53 pp.  mathscinet  zmath
4. W. L. Gan and V. Ginzburg, “Quantization of Slodowy slices”, Int. Math. Res. Not., 2002, no. 5, 243–255  crossref  mathscinet  zmath
5. A. Joseph, “Gelfand–Kirillov dimension for the annihilators of simple quotients of Verma modules”, J. London Math. Soc. (2), 18:1 (1978), 50–60  crossref  mathscinet  zmath
6. I. Losev, “Quantized symplectic actions and $W$-algebras”, J. Amer. Math. Soc., 23:1 (2010), 35–59  crossref  mathscinet  zmath  elib
7. I. Losev, “Finite-dimensional representations of $W$-algebras”, Duke Math. J., 159:1 (2011), 99–143  crossref  mathscinet  zmath  elib
8. I. Losev, “1-dimensional representations and parabolic induction for W-algebras”, Adv. Math., 226:6 (2011), 4841–4883  crossref  mathscinet  zmath  elib
9. I. Losev, “On the structure of the category $\mathcal O$ for $W$-algebras”, Geometric methods in representation theory. II, Sémin. Congr., 24, Soc. Math. France, Paris, 2012, 353–370  mathscinet  zmath
10. I. Losev, “Dimensions of irreducible modules over W-algebras and Goldie ranks”, Invent. Math., 200:3 (2015), 849–923  crossref  mathscinet  zmath  adsnasa  elib
11. I. Losev, “Quantizations of regular functions on nilpotent orbits”, Bull. Inst. Math. Acad. Sin. (N.S.), 13:2 (2018), 199–225  mathscinet  zmath
12. I. Losev and V. Ostrik, “Classification of finite-dimensional irreducible modules over $W$-algebras”, Compos. Math., 150:6 (2014), 1024–1076  crossref  mathscinet  zmath  elib
13. J. C. McConnell and J. C. Robson, Noncommutative Noetherian rings, Graduate Studies in Mathematics, 30, revised ed., Amer. Math. Soc., Providence, RI, 2001  crossref  mathscinet  zmath
14. W. M. McGovern, Completely prime maximal ideals and quantization, Mem. Amer. Math. Soc., 108, no. 519, 1994  mathscinet
15. A. S. Merkurjev, “Equivariant $K$-theory”, Handbook of $K$-theory, v. 1, 2, Springer, Berlin, 2005, 925–954  crossref  mathscinet  zmath
16. I. A. Panin, “On the algebraic $K$-theory of twisted flag varieties”, $K$-Theory, 8:6 (1994), 541–585  crossref  mathscinet  zmath
17. St. Petersburg Math. J., 10:1 (1999), 69–101  mathnet  mathscinet  zmath
18. A. Premet, “Special transverse slices and their enveloping algebras”, With an appendix by Serge Skryabin, Adv. Math., 170:1 (2002), 1–55  crossref  mathscinet  zmath
19. A. Premet, “Enveloping algebras of Slodowy slices and Goldie rank”, Transform. Groups, 16:3 (2011), 857–888  crossref  mathscinet  zmath
20. R. B. Warfield, Jr., “Prime ideals in ring extensions”, J. London Math. Soc. (2), 28:3 (1983), 453–460  crossref  mathscinet  zmath


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