Benanti, Drensky: Polynomial identities of nil algebras of bounded index

Benanti, Francesca and Drensky, Vesselin:
Polynomial identities of nil algebras of bounded index
Bollettino dell'Unione Matematica Italiana Serie 8 2-B (1999), fasc. n.3, p. 673-691, Unione Matematica Italiana (English)
pdf (280 Kb), djvu (240 Kb). | MR1719534 | Zbl 0943.16007

Sunto

Lo scopo di questo lavoro è di dare una nuova descrizione del $T$-ideale generato dalla nil-identità $x^{n}=0$ come immagine omeomorfa della $n$-esima potenza tensoriale simmetrica dell'algebra associativa libera $K \langle X \rangle$ su un campo $K$ di caratteristica $0$. Come applicazione calcoliamo il carattere delle conseguenze multilineari di grado $\leq n+2$ dell'identità $x^{n}=0$.

Referenze Bibliografiche

[1] S. ABEASIS - M. PITTALUGA , On a minimal set of generators for the invariants of $3 \times 3$ matrices, Commun. Algebra, 17 (1989), 487-499. | MR 978487 | Zbl 0672.16016

[2] F. BENANTI - V. DRENSKY , On the consequences of the standard polynomial, Commun. Algebra (to appear). | MR 1661241 | Zbl 0919.16016

[3] A. BERELE , Homogeneous polynomial identities, Isr. J. Math., 42 (1982), 258-272. | MR 687131 | Zbl 0522.16015

[4] V. DRENSKY , Representations of the symmetric group and varieties of linear algebras (Russian), Mat. Sb., 115 (1981), 98-115. Translation: Math. USSR Sb., 43 (1981), 85-101. | MR 618589 | Zbl 0465.17007

[5] V. DRENSKY , Computational techniques for PI-algebras, Banach Center Publ., 26, Topics in Algebra, Part 1: Rings and Representations of Algebras, Polish Scientific Publishers, Warshaw (1990), 17-44. | MR 1171223 | Zbl 0724.16012

[6] J. DUBNOV , Sur une généralisation de l'équation de Hamilton-Cayley et sur les invariants simultanés de plusieurs affineurs, Proc. Seminar on Vector and Tensor Analysis, Mechanics Research Inst., Moscow State Univ., 2/3 (1935), 351-367 (see also Zbl. für Math., 12 (1935), p. 176). | Zbl 0012.17604

[7] J. DUBNOV - V. IVANOV , Sur l'abaissement du degré des polynômes en affineurs, C.R. (Doklady) Acad. Sci. USSR, 41 (1943), 96-98 (see also MR, 6 (1945), p. 113, Zbl. für Math., 60 (1957), p. 33). | MR 11069 | Zbl 0060.03308

[8] E. FORMANEK , Generating the ring of matrix invariants, Lect. Notes in Math., 1195, Springer Verlag, Berlin-Heidelberg-New York (1986), 73-82. | MR 859385 | Zbl 0602.16017

[9] E. FORMANEK , The Polynomial Identities and Invariants of $n \times n$ Matrices, CBMS Regional Conf. Series in Math., 78, Published for the Confer. Board of the Math. Sci., Washington DC, AMS, Providence, RI (1991). | MR 1088481 | Zbl 0714.16001

[10] G. HIGMAN , On a conjecture of Nagata, Proc. Camb. Philos. Soc., 52 (1956), 1-4. | MR 73581 | Zbl 0072.02502

[11] G. JAMES - A. KERBER , The Representation Theory of the Symmetric Group, Encyclopedia of Math. and Its Appl., 16, Addison-Wesley, Reading, Mass. (1981). | MR 644144 | Zbl 0491.20010

[12] P. E. KOSHLUKOV , Polynomial identities for a family of simple Jordan algebras, Commun. Algebra, 16 (1988), 1325-1371. | MR 941174 | Zbl 0661.17027

[13] E.N. KUZ'MIN , On the Nagata - Higman theorem, in Mathematical Structures, Computational Mathematics, Mathematical Modelling, Proc. Deducated to the 60th Birthday of Acad. L. Iliev, Sofia (1975), 101-107. | Zbl 0592.20040

[14] I. G. MACDONALD , Symmetric Functions and Hall Polynomials, Second edition, Oxford Univ. Press (Clarendon), Oxford (1995). | MR 1354144 | Zbl 0824.05059

[15] M. NAGATA , On the nilpotency of nil algebras, J. Math. Soc. Japan, 4 (1952), 296-301. | fulltext mini-dml | MR 53088 | Zbl 0049.02402

[16] C. PROCESI , The invariant theory of $n \times n$ matrices, Adv. in Math., 19 (1976), 306-381. | MR 419491 | Zbl 0331.15021

[17] C. PROCESI , Trace indentities and standard diagrams, in Ring Theory, Lect. Notes in Math., 51, Marcel Dekker, New York (1979), 191-218. | MR 563295 | Zbl 0432.15020

[18] U. P. RAZMYSLOV , Trace identities of full matrix algebras over a field of characteristic zero (Russian), Izv. Akad. Nauk SSSR, Ser. Mat., 38 (1974), 723-756. Translation: Math. USSR Izv., 8 (1974), 723-760. | MR 506414 | Zbl 0311.16016

[19] K. S. SIBERSKII , Algebraic invariants for a set of matrices (Russian), Sib. Mat. Zh., 9 (1) (1968), 152-164. Translation: Siber. Math. J., 9 (1968), 115-124. | Zbl 0273.15024

[20] R. M. THRALL , On symmetrized Kronecker powers and the structure of the free Lie ring, Trans. Amer. Math. Soc., 64 (1942), 371-388. | MR 6149 | Zbl 0061.04201

[21] M. R. VAUGHAN-LEE , An algorithm for computing graded algebras, J. Symbolic Comp., 16 (1993), 345-354. | MR 1263872 | Zbl 0801.16025

[22] L. A. VLADIMIROVA - V. DRENSKY , Varieties of associative algebras with identity of third degree, Pliska, Stud. Math. Bulg., 8 (1986), 144-157. | MR 866654 | Zbl 0664.16015

[23] H. WEYL , The Classical Groups, Their Invariants and Representations, Princeton Univ. Press, Princeton, N.J. (1946). | MR 1488158 | Zbl 1024.20502

bdim: Biblioteca Digitale Italiana di Matematica

Un progetto SIMAI e UMI

Referenza completa

Sunto

Referenze Bibliografiche