14.08.2013 Views

TH`ESE A NEW INVARIANT OF QUADRATIC LIE ALGEBRAS AND ...

TH`ESE A NEW INVARIANT OF QUADRATIC LIE ALGEBRAS AND ...

TH`ESE A NEW INVARIANT OF QUADRATIC LIE ALGEBRAS AND ...

SHOW MORE
SHOW LESS

Create successful ePaper yourself

Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.

Bibliography<br />

[Bou71] , Eléments de Mathématiques. Groupes et Algèbres de Lie, Vol. Chapitre I, Algèbres de Lie,<br />

Hermann, Paris, 1971. ↑133, 134<br />

[BP89] H. Benamor and G. Pinczon, The graded Lie algebra structure of Lie superalgebra deformation theory,<br />

Lett. Math. Phys. 18 (1989), no. 4, 307 – 313. ↑62, 64, 66, 74<br />

[Bur06] D. Burde, Classical r-matrices and Novikov algebras, Geom. Dedicata 122 (2006), 145–157. ↑116<br />

[CM93] D. H. Collingwood and W. M. McGovern, Nilpotent Orbits in Semisimple Lie Algebras, Van Nostrand<br />

Reihnhold Mathematics Series, New York, 1993. ↑viii, 3, 5, 8, 10, 12<br />

[Dix74] J. Dixmier, Algèbres enveloppantes, Cahiers scientifiques, fasc.37, Gauthier-Villars, Paris, 1974. ↑35<br />

[DPU] M. T. Duong, G. Pinczon, and R. Ushirobira, A new invariant of quadratic Lie algebras, Alg. Rep.<br />

Theory (to appear). ↑<br />

[FK94] J. Faraut and A. Koranyi, Analysis on symmetric cones, Oxford Mathematical Monographs, 1994. ↑99<br />

[FS87] G. Favre and L. J. Santharoubane, Symmetric, invariant, non-degenerate bilinear form on a Lie algebra,<br />

J. Algebra 105 (1987), 451–464. ↑viii, 17, 19, 20, 39<br />

[GD79] I. M. Gel’fand and I. Y. Dorfman, Hamiltonian operators and algebraic structures related to them,<br />

Funct. Anal. Appl 13 (1979), no. 4, 248 – 262. ↑xvii<br />

[Gié04] P. A. Gié, Nouvelles structures de Nambu et super-théorème d’Amitsur-Levizki, Thèse de l’Université<br />

de Bourgogne (2004), 153 pages. ↑61, 64, 66<br />

[Hum72] J. Humphreys, Introduction to Lie Algebras and Representation Theory, Graduate Texts in Maths.,<br />

Springer-Verlag, New York, 1972. ↑6<br />

[Hum95] , Conjugacy classes in semisimple algebraic groups, Mathematical Surveys and Monographs,<br />

vol. 43, American Mathematical Society, 1995. ↑3<br />

[Jac51] N. Jacobson, General representation theory of Jordan algebras, Trans. Amer. Math. Soc 70 (1951),<br />

509–530. ↑<br />

[Kac85] V. Kac, Infinite-dimensional Lie algebras, Cambrigde University Press, New York, 1985. ↑vii, 17, 19<br />

[Kos50] J-L. Koszul, Homologie et cohomologie des algèbres de Lie, Bulletin de la S. M. F 78 (1950), 65–127.<br />

↑<br />

[Mag10] L. Magnin, Determination of 7-dimensional indecomposable Lie algebras by adjoining a derivation<br />

to 6-dimensional Lie algebras, Alg. Rep. Theory 13 (2010), 723 – 753. ↑36<br />

[MPU09] I. A. Musson, G. Pinczon, and R. Ushorobira, Hochschild Cohomology and Deformations of Clifford-<br />

Weyl Algebras, SIGMA 5 (2009), 27 pp. ↑xii, 61, 62<br />

[MR85] A. Medina and P. Revoy, Algèbres de Lie et produit scalaire invariant, Ann. Sci. École Norm. Sup. 4<br />

(1985), 553–561. ↑vii, 17, 19<br />

[NR66] A. Nijenhuis and R. W. Richardson, Cohomology and deformations in graded Lie algebras, Bull.<br />

Amer. Math. Soc. 72 (1966), 1–29. ↑63<br />

[Oom09] A. Ooms, Computing invariants and semi-invariants by means of Frobenius Lie algebras, J. of Algebra<br />

4 (2009), 1293 – 1312. ↑36<br />

[Ova07] G. Ovando, Two-step nilpotent Lie algebras with ad-invariant metrics and a special kind of skewsymmetric<br />

maps, J. Algebra and its Appl. 6 (2007), no. 6, 897–917. ↑xi, xii, 59, 108, 119<br />

[PU07] G. Pinczon and R. Ushirobira, New Applications of Graded Lie Algebras to Lie Algebras, Generalized<br />

Lie Algebras, and Cohomology, J. Lie Theory 17 (2007), no. 3, 633 – 668. ↑vi, vii, 17, 18, 22, 27, 28,<br />

35, 36, 59, 66<br />

[Sam80] H. Samelson, Notes on Lie algebras, Universitext, Springer-Verlag, 1980. ↑132<br />

142

Hooray! Your file is uploaded and ready to be published.

Saved successfully!

Ooh no, something went wrong!