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On the importance of being primitive
DOI:
https://doi.org/10.15446/recolma.v53nsupl.84009Schlagworte:
primitive ideals, Dixmier-Moeglin equivalence, prime spectrum (en)Ideales primitivos, Equivalencia de Dixmier-Moeglin, espectro primo (es)
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Literaturhinweise
G. Abrams, J. P. Bell, and K. M Rangaswamy, The Dixmier-Moeglin equivalence for Leavitt path algebras, Algebr. Represent. Theory 15 (2002), no. 3, 407-425.
M. Artin and J. T. Stafford, Noncommutative graded domains with quadratic growth, Invent. Math. 122 (1995), no. 2, 231-276.
Y. A. Bachturin, Identities in the universal envelopes of Lie algebras. Collection of articles dedicated to the memory of Hanna Neumann, IX, J. Austral. Math. Soc. 18 (1974), 10-21.
J. Bell, S. Launois, and B. Nolan, A strong Dixmier-Moeglin equivalence for quantum Schubert cells, J. Algebra 487 (2017), 269-293.
J. Bell, S. Launois, O. León Sánchez, and R. Moosa, Poisson algebras via model theory and differential-algebraic geometry, J. Eur. Math. Soc. (JEMS) 19 (2017), no. 7, 2019-2049.
J. Bell, D. Rogalski, and S. J. Sierra, The Dixmier-Moeglin equivalence for twisted homogeneous coordinate rings, Israel J. Math. 180 (2010), 461-507.
J. Bell, O. León Sánchez, and R. Moosa, D-groups and the Dixmier-Moeglin equivalence, Algebra Number Theory 12 (2018), no. 2, 343-378.
J. P. Bell and D. Ghioca, Periodic subvarieties of semiabelian varieties and annihilators of irreducible representations, Adv. Math. 349 (2019), 459-487.
J. P. Bell and W. H. Leung, The Dixmier-Moeglin equivalence for co-commutative Hopf algebras of finite Gelfand-Kirillov dimension, Algebr. Represent. Theory 17 (2014), no. 6, 1843-1852.
J. P. Bell, X. Wang, and D. Yee, The Dixmier-Moeglin equivalence, Morita equivalence, and homeomorphism of spectra, J. Algebra 534 (2019), 228-244.
J. P. Bell, K. Wu, and S. Wu, The Dixmier-Moeglin equivalence for extensions of scalars and Ore extensions, Groups, rings, group rings, and Hopf algebras, 1{14, Contemp. Math., 688, Amer. Math. Soc., Providence, RI, 2017.
G. M. Bergman, A ring primitive on the right but not on the left, Proc. Amer. Math. Soc. 15 (1964), 473-475.
K. Brown, S. O'Hagan, J. Zhang, and G. Zhuang, Connected Hopf algebras and iterated Ore extensions, J. Pure Appl. Algebra 219 (2015), no. 6, 2405-2433.
K. A. Brown, The Nullstellensatz for certain group rings, J. London Math. Soc. 26 (1982), no. 3, 425-434.
K. A. Brown, P. A.A.B. Carvalho, and J. Matczuk, Simple modules and their essential extensions for skew polynomial rings, Preprint, available online at ArXiv:1705.06596.
K. A. Brown and P. Gilmartin, Hopf algebras under finiteness conditions, Palest. J. Math. 3 (2014), Special issue, 356-365.
K. A. Brown and K. R. Goodearl, Lectures on algebraic quantum groups, Advanced Courses in Mathematics. CRM Barcelona. Birkhäuser Verlag, Basel, 2002.
K. A. Brown and I. Gordon, Poisson orders, symplectic reflection algebras and representation theory, J. Reine Angew. Math. 559 (2003), 193-216.
K. Casteels, Quantum matrices by paths, Algebra Number Theory 8 (2014), no. 8, 1857-19129.
G. Cauchon, Effacement des dérivations et spectres premiers des algèbres quantiques, J. Algebra 260 (2003), no. 2, 476-518.
J. Dixmier, Idéaux primitifs dans les algèbres enveloppantes, J. Algebra 48 (1977), 96-112.
D. Eisenbud, Commutative algebra. With a view toward algebraic geometry, Graduate Texts in Mathematics, 150. Springer-Verlag, New York, 1995.
K. R. Goodearl and R. B. Warfield Jr., Primitivity in differential operator rings, Math. Z. 180 (1982), no. 4, 503-523.
K. R. Goodearl and R. B. Warfield Jr., An introduction to noncommutative noetherian rings, Second edition. London Mathematical Society Student Texts, 61. Cambridge University Press, Cambridge, 2004.
K. R. Goodearl and S. Launois, The Dixmier-Moeglin equivalence and a Gelfand-Kirillov problem for Poisson polynomial algebras, Bull. Soc. Math. France 139 (2011), no. 1, 1-39.
K. R. Goodearl, S. Launois, and T. H. Lenagan, Torus-invariant prime ideals in quantum matrices, totally nonnegative cells and symplectic leaves, Math. Z. 269 (2011), no. 1-2, 29-45.
K. R. Goodearl and E. S. Letzter, The Dixmier-Moeglin equivalence in quantum coordinate rings and quantized Weyl algebras, Trans. Amer. Math. Soc. 352 (2000), no. 3, 1381-1403.
K. R. Goodearl and J. J. Zhang, Noetherian Hopf algebra domains of Gelfand-Kirillov dimension two, J. Algebra 324 (2010), no. 11, 3131-3168.
R. S. Irving, Noetherian algebras and nullstellensatz, Séminaire d'Algèbre Paul Dubreil 31 me année (Paris, 1977-1978). Lecture Notes in Math., 740, Springer, Berlin (1979), 80-87.
R. S. Irving, Primitive ideals of certain Noetherian algebras, Math. Z. 169 (1979), no. 1, 77-92.
R. S. Irving, Primitive Noetherian algebras with big centers, Proc. Amer. Math. Soc. 129 (2001), no. 6, 1587-1593.
N. Jacobson, Structure theory for algebraic algebras of bounded degree, Ann. Math. 46 (1945), 695-707.
A. V. Jategaonkar, Relative Krull dimension and prime ideals in right Noetherian rings, Comm. Algebra 2 (1974), 429-468.
D. A. Jordan, Primitive Ore extensions, Glasgow Math. J. 18 (1977), no. 1, 93-97.
D. A. Jordan, Primitivity in skew Laurent polynomial rings and related rings, Math. Z. 213 (1993), no. 3, 353-371.
D. A. Jordan and S.-Q. Oh, Poisson spectra in polynomial algebras, J. Algebra 400 (2014), 56-71.
M. Kontsevich, Deformation quantization of Poisson manifolds, Lett. Math. Phys. 66 (2003), no. 3, 157-216.
G. R. Krause and T. H. Lenagan, Growth of algebras and gelfand-kirillov dimension, Revised edition. Graduate Studies in Mathematics, 22. American Mathematical Society, Providence, RI.
S. Launois and C. Lecoutre, Poisson deleting derivations algorithm and Poisson spectrum, Comm. Algebra 45 (2017), no. 3, 1294-1313.
A. Leroy and J. Matczuk, Primitivity of skew polynomial and skew Laurent polynomial rings, Comm. Algebra 24 (1996), no. 7, 2271-2284.
A. Leroy and J. Matczuk, On q-skew iterated Ore extensions satisfying a polynomial identity, J. Algebra Appl. 10 (2011), no. 4, 771-781.
E. Letzter, Primitive ideals in finite extensions of Noetherian rings, J. London Math. Soc. 39 (1989), no. 2-3, 427-435.
M. Lorenz, Primitive ideals of group algebras of supersoluble groups, Math. Ann. 225 (1977), no. 2, 115-122.
M. Lorenz, Group actions and rational ideals, Algebra Number Theory 2 (2008), no. 4, 467-499.
M. Lorenz, Algebraic group actions on noncommutative spectra, Transform. Groups 14 (2009), no. 3, 649-675.
M. Lorenz, On the stratification of noncommutative prime spectra, Proc. Amer. Math. Soc. 142 (2014), no. 9, 3013-3017.
C. Moeglin, Idéaux bilatères des algèbres enveloppantes, Bull. Soc. Math. France 108 (1980), 143-186.
C. Moeglin and R. Rentschler, Orbites d'un groupe algébrique dans l'espace des idéaux rationnels d'une algèbre enveloppante, Bull. Soc. Math. France 109 (1981), no. 2-3, 403-426.
C. Moeglin and R. Rentschler, Idéaux g-rationnels, Rang de Goldie. Unpublished manuscript, 1986.
S.-Q. Oh, Quantum and Poisson structures of multi-parameter symplectic and Euclidean spaces, J. Algebra 319 (2008), no. 11, 4485-4535.
, Poisson Hopf algebra related to a twisted quantum group, Comm. Algebra 45 (2017), no. 1, 76-104.
L. H. Rowen, Ring theory. vol. ii., Pure and Applied Mathematics, 128. Academic Press, Inc., Boston, MA, 1988.
L. H. Rowen, Graduate algebra: noncommutative view, Graduate Studies in Mathematics, 91. American Mathematical Society, Providence, RI, 2008.
R. L. Snider, Primitive ideals in group rings of polycyclic groups, Proc. Amer. Math. Soc. 57 (1976), no. 1, 8-10.
N. Vonessen, Actions of algebraic groups on the spectrum of rational ideals, J. Algebra 182 (1996), no. 2, 383-400.
N. Vonessen, Actions of algebraic groups on the spectrum of rational ideals. II., J. Algebra 208 (1998), no. 1, 216-261.
M. Yakimov, Invariant prime ideals in quantizations of nilpotent Lie algebras, Proc. Lond. Math. Soc.(3) 101 (2010), no. 2, 454-476.
M. Yakimov, On the spectra of quantum groups, Mem. Amer. Math. Soc. 229 (2014), no. 1078.
A. E. Zalesskii, The irreducible representations of finitely generated nilpotent groups without torsion, Mat. Zametki 9 (1971), 199-210.
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3. K. Brown, J. Stafford. (2024). Recent Advances in Noncommutative Algebra and Geometry. Contemporary Mathematics. 801, p.51. https://doi.org/10.1090/conm/801/16036.
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5. Jason Bell, Léon Burkhardt, Nicholas Priebe. (2024). Recent Advances in Noncommutative Algebra and Geometry. Contemporary Mathematics. 801, p.1. https://doi.org/10.1090/conm/801/16035.
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