nLab Anthony Joseph

Anthony Joseph is an algebraist at the Weizmann Institute of Science. His interests include universal enveloping algebras, quantum groups and invariant theory.

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Selected writings

Joseph’s major monograph is

• Anthony Joseph, Quantum groups and their primitive ideals, Springer (1995)

On Jantzen conjecture

• Anthony Joseph, Towards the Jantzen conjecture, Compositio Mathematica 40:1 (1980) 35–67 (numdam pdf); Towards the Jantzen conjecture, II, Cornpositio Math. 40 (1980) 69–78

• Anthony Joseph, On the annihilators of the simple subquotients of the principal series, Ann. Sci. École Norm. Sup.10 (1977) 419–439

On prime spectra of universal enveloping algebras

• Anthony Joseph, A preparation theorem for the prime spectrum of a semisimple Lie algebra, J. Algebra 48:2 (1977) 241–289 doi

On the BGG resolution:

• Ofer Gabber, A. Joseph, On the Bernstein-Gelfand-Gelfand resolution and the Duflo sum formula, Compositio Math. 43 (1981) 107–131

On Kazhdan-Lusztig conjecture?

• Ofer Gabber, Anthony Joseph, Towards the Kazhdan-Lusztig conjecture, Annales scientifiques de l’École Normale Supérieure 14.3 (1981): 261–302 numdam eudml

On quantum groups:

• Anthony Joseph, Gail Letzter, Local finiteness of the adjoint action for quantized enveloping algebra, J. Algebra 153 2 (1992) 289–318

• Anthony Joseph, Gail Letzter, Separation of variables for quantized enveloping algebras, Amer. J. Math. 116 1 (1994) 127–177 doi:10.2307/2374984

• Anthony Joseph, Faithfully flat embeddings for minimal primitive quotients of quantized enveloping algebras, 79–106 in: Israel Mathematics Conference Proceedings 7, Bar-Ilan University 1993; 176 pp. Quantum Deformations of Algebras and Their Representations, ed. Anthony Joseph, Steven Shnider.

On Goldie rank

• Anthony Joseph, Lance W. Small, An additivity principle for Goldie rank, Israel J. Math. 31 (1978) 105–114 doi
• Anthony Joseph, Kostant’s problem, Goldie rank and the Gelfand-Kirillov conjecture, Invent. Math. 56 (1980) 191–213

On Goldie rank for universal enveloping algebras

• Anthony Joseph, Goldie rank in the enveloping algebra of a semisimple Lie algebra, I, J. Algebra 65:2 (1980) 269–283 doi; Goldie rank in the enveloping algebra of a semisimple Lie algebra II, J. Algebra 65 (1980) 284–306

• Anthony Joseph, On the annihilators of the simple subquotients of the principal series Ann. Sci. École Norm. Sup.10, 419–439 (1977)

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