Invariant Ideals and Matsushima's Criterion

REFERENCES

• Arzhantsev , I. V. ( 2003 ). Algebras with finitely generated invariant subalgebras . Ann. Inst. Fourier (Grenoble) ( 53 : 2 ): 379 – 398 .
   Web of Science ®Google Scholar
• Bialynicki-Birula , A. ( 1963 ). On homogeneous affine spaces of linear algebraic groups . Amer. J. Math. 85 : 577 – 582 .
   Web of Science ®Google Scholar
• Bialynicki-Birula , A. , Hochschild , G. , Mostow , G. D. ( 1963 ). Extensions of representations of algebraic linear groups . Amer. J. Math. 85 : 131 – 144 .
   Web of Science ®Google Scholar
• Cline , E. , Parshall , B. , Scott , L. ( 1977 ). Induced modules and affine quotients . Math. Ann. 230 : 1 – 14 .
   Google Scholar
• Grosshans , F. D. ( 1997 ). Algebraic homogeneous spaces and invariant theory . In: Lecture Notes in Math . Vol. 1673 . Berlin : Springer-Verlag .
   Google Scholar
• Humphreys , J. E. ( 1972 ). Introduction to Lie algebras and representation theory . In: Graduate Texts in Math . Vol. 9 . New York, Berlin : Springer-Verlag .
   Google Scholar
• Humphreys , J. E. ( 1975 ). Linear algebraic groups . In: Graduate Texts in Math . Vol. 21 . New York, Heidelberg, Berlin : Springer-Verlag .
   Google Scholar
• Luna , D. ( 1973 ). Slices étales . Bull. Soc. Math. Fr. Memoire 33 : 81 – 105 .
   Google Scholar
• Matsushima , Y. ( 1960 ). Espaces homogénes de Stein des groupes de Lie complexes . Nagoya Math. J. 16 : 205 – 218 .
   Google Scholar
• Onishchik , A. L. ( 1960 ). Complex hulls of compact homogeneous spaces . Dokl. Akad. Nauk SSSR ( 130 : 4 ): 726 – 729 (Russian); English Transl. Soviet Math. Dokl. 1 : 88 – 91 .
   Google Scholar
• Popov , V. L. , Vinberg , E. B. ( 1989 ). Invariant theory . In: Itogi Nauki i Tekhniki , Sovrem. Probl. Mat. Fund. Naprav. Vol. 55, VINITI, Moscow (Russian); English Transl. (1994). In: Encyclopedia of Math. Sciences. Algebraic Geometry IV, Vol. 55 . Berlin : Springer-Verlag .
   Google Scholar
• Richardson , R. W. (1977). Affine coset spaces of reductive algebraic groups. Bull. London Math. Soc. (9:1):38–41.
   Google Scholar
• Springer , T. A. ( 1977 ). Invariant theory . In: Lecture Notes in Math . Vol. 585 . Berlin, Heidelberg, New York : Springer-Verlag .
   Google Scholar
• Vinberg , E. B. ( 2000 ). On stability of actions of reductive algebraic groups . In: Fong Yuen , A. A. , Mikhalev , E. , Zelmanov , eds. Lie Algebras, Rings and Related Topics . Hong Kong Ltd. : Springer-Verlag , pp. 188 – 202 .
   Google Scholar
• Communicated by J. Alev.
   Google Scholar