×

zbMATH — the first resource for mathematics

Intermediate growth in finitely presented algebras. (English) Zbl 1380.16021

MSC:
16P90 Growth rate, Gelfand-Kirillov dimension
16S30 Universal enveloping algebras of Lie algebras
17B70 Graded Lie (super)algebras
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Bahturin, Yu. A., Identical Relations in Lie Algebras, (1987), VNU Science Press, Utrecht
[2] Bakhturin, Yu. A.; Drenski, V. S., The identities of solvable colored super Lie algebras, Algebra Logika, 26, 4, 403-418, (1987) · Zbl 0645.17014
[3] Bartholdi, L.; Grigorchuk, R. I., Computational and Geometric Aspects of Modern Algebra (Edinburgh, 1998), 275, Lie methods in growth of groups and groups of finite width, 1-27, (2000), Cambridge University Press, Cambridge · Zbl 1032.20026
[4] Baumslag, G., Subalgebras of finitely presented solvable Lie algebras, J. Algebra, 45, 2, 295-305, (1977) · Zbl 0364.17005
[5] Bereznyĭ, A. E., Discrete subexponential groups, Zap. Nauchn. Sem.-Leningrad. Otdel. Mat. Inst. Steklov. (LOMI), 123, 155-166, (1983) · Zbl 0509.16007
[6] Gelfand, I. M.; Kirillov, A. A., On fields connected with the enveloping algebras of Lie algebras, Dokl. Akad. Nauk SSSR, 167, 503-505, (1966)
[7] Gelfand, I. M.; Kirillov, A. A., Sur LES corps liés aux algèbres enveloppantes des algèbres de Lie, Publ. Math. Inst. Hautes Études Sci., 31, 5-19, (1966) · Zbl 0144.02104
[8] Grigorchuk, R. I., On the Milnor problem of group growth, Dokl. Akad. Nauk SSSR, 271, 1, 30-33, (1983)
[9] Grigorchuk, R. I., Construction of \(p\)-groups of intermediate growth that have a continuum of factor-groups, Algebra Logika, 23, 4, 383-394, (1984) · Zbl 0573.20037
[10] Grigorchuk, R., On the gap conjecture concerning group growth, Bull. Math. Sci., 4, 1, 113-128, (2014) · Zbl 1323.20035
[11] Gromov, M., Groups of polynomial growth and expanding maps, Publ. Math. Inst. Hautes Études Sci., 53, 53-73, (1981) · Zbl 0474.20018
[12] Jacobson, N., Lie Algebras, (1962), Interscience, New York, London · Zbl 0121.27504
[13] Koçak, D., Finitely presented quadratic algebras of intermediate growth, Algebra Discrete Math., 20, 1, 69-88, (2015) · Zbl 1350.16017
[14] Lavrik-Männlin, A. A., On some semigroups of intermediate growth, Internat. J. Algebra Comput., 11, 5, 565-580, (2001) · Zbl 1025.20041
[15] Leites, D.; Poletaeva, E., Defining relations for classical Lie algebras of polynomial vector fields, Math. Scand., 81, 1, 5-19, (1998) · Zbl 0893.17003
[16] Lewin, J., A matrix representation for associative algebras. I, II, Trans. Amer. Math. Soc., 188, 293-308, (1974) · Zbl 0343.16002
[17] Lichtman, A. I., Growth in enveloping algebras, Israel J. Math., 47, 4, 296-304, (1984) · Zbl 0552.17006
[18] Milnor, J., A note on curvature and fundamental group, J. Differential Geom., 2, 1-7, (1968) · Zbl 0162.25401
[19] Petrogradskiĭ, V. M., Some type of intermediate growth in Lie algebras, Uspekhi Mat. Nauk, 48, 5, 181-182, (1993) · Zbl 0823.17015
[20] Petrogradsky, V. M., Intermediate growth in Lie algebras and their enveloping algebras, J. Algebra, 179, 2, 459-482, (1996) · Zbl 0964.17005
[21] Petrogradsky, V. M., Growth of finitely generated polynilpotent Lie algebras and groups, generalized partitions, and functions analytic in the unit circle, Internat. J. Algebra Comput., 9, 2, 179-212, (1999) · Zbl 0931.17007
[22] Ramanujan, S.; Hardy, G. H.; Seshu Aiyar, P. V.; Wilson, B. M., Collected Papers of Srinivasa Ramanujan, Asymptotic formulae in combinatory analysis, 276-309, (2000), AMS Chelsea Publishing, Providence, RI
[23] Šmel\(\prime\)kin, A. L., Wreath products of Lie algebras, and their application in group theory, Tr. Mosk. Mat. Obš., 29, 247-260, (1973)
[24] Smith, M. K., Universal enveloping algebras with subexponential but not polynomially bounded growth, Proc. Amer. Math. Soc., 60, 1, 22-24, (1976) · Zbl 0347.17005
[25] Stewart, I., Finitely presented infinite-dimensional simple Lie algebras, Arch. Math. (Basel), 26, 5, 504-507, (1975) · Zbl 0314.17010
[26] Švarc, A. S., A volume invariant of coverings, Dokl. Akad. Nauk SSSR, 105, 32-34, (1955) · Zbl 0066.15903
[27] Ufnarovskiĭ, V. A., Poincaré series of graded algebras, Mat. Zametki, 27, 1, 21-32, (1980)
[28] Ufnarovskiĭ, V. A., Current Problems in Mathematics. Fundamental Directions, Vol. 57 (Russian), Combinatorial and asymptotic methods in algebra, 5-177, (1990), Moscow · Zbl 0706.16001
[29] Wolf, J. A., Growth of finitely generated solvable groups and curvature of riemanniann manifolds, J. Differential Geom., 2, 421-446, (1968) · Zbl 0207.51803
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.