The scientific legacy of Miloslav Havlíček

Authors

  • Rutwig Campoamor-Stursberg Universidad Complutense de Madrid, Instituto de Matem´atica Interdisciplinar, Plaza de Ciencias 3, E-28040 Madrid, Spain

DOI:

https://doi.org/10.14311/AP.2025.65.0500

Keywords:

realisations of Lie algebras, Lie gradings, quantum groups, differential equations, quantum mechanics

Abstract

We review the main research achievements of Miloslav Havl´ıˇcek in algebraic methods in Quantum Theory, his extensive work on realisations of Lie algebras and superalgebras and their representation theory, quantum groups and differential equations.

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References

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M. Havl´ıˇcek, W. Lassner. Matrix canonical realizations of the Lie algebra u(p, q). Reports on Mathematical Physics 12(1):1–8, 1977. https://doi.org/10.1016/0034-4877(77)90040-4

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P. Exner, M. Havlicek, W. Lassner. Boson representations of classical Lie algebras. In International Conference on Operator Algebras, Ideals and their Applications in Theoretical Physics, pp. 277–278. 1977.

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J. Blank, M. Havl´ıˇcek. Irreducible *-representations of Lie superalgebras B(0, n) with finite-degenerated vacuum. Journal of Mathematical Physics 27(12):2823–2831, 1986. https://doi.org/10.1063/1.527257

J. Blank, M. Havl´ıˇcek. Irreducible *-representations of the Lie superalgebras B(0, n) with finite-degenerated vacuum. II. Journal of Mathematical Physics 29(3):546–559, 1988. https://doi.org/10.1063/1.528048

J. Blank, M. Havl´ıˇcek. On the tensor product of supersingleton representations of osp(1, 2n). Czechoslovak Journal of Physics B 39(11):1192–1207, 1989. https://doi.org/10.1007/BF01605320

J. Blank, M. Havl´ıˇcek. On the tensor product of supersingleton representations of Lie superalgebras osp(1, 2n). In Selected Topics in Quantum Field Theory and Mathematical Physics, pp. 190–196. World Scientific, 1989.

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ˇC. Burd´ık, M. Havl´ıˇcek, A. Vanˇcura. Irreducible highest weight representations of quantum groups Uq(gl(n,C)). Communications in Mathematical Physics 148(2):417–423, 1992. https://doi.org/10.1007/BF02100869

M. Havl´ıˇcek, E. Pelantov´a, A. Klimyk. Nonstandard Uq(so3) and Uq(so4): Tensor products of representations, oscillator realizations and roots of unity. Czechoslovak Journal of Physics 47(1):13–16, 1997. https://doi.org/10.1023/A:1021431709238

M. Havl´ıˇcek, E. Pelantov´a. Santilli-Fairlie algebra Uq(so3): Tensor products of representations, oscillator realizations and roots of unity. Hadronic Journal 20(6):603–614, 1997.

M. Havl´ıˇcek, S. Poˇsta, A. U. Klimyk. Representations of the cyclically symmetric q-deformed algebra Uq(so3). Czechoslovak Journal of Physics 48(11):1347–1353, 1998. https://doi.org/10.1023/A:1021692803323

M. Havl´ıˇcek, A. U. Klimyk, E. Pelantov´a. Representations of the q-deformed algebra Uq(so4) for q a root of unity. Methods in Functional Analysis and Topology 4(3):39–44, 1998.

M. Havl´ıˇcek, A. U. Klimyk, S. Poˇsta. Representations of the cyclically symmetric q-deformed algebra soq(3). Journal of Mathematical Physics 40(4):2135–2161, 1999. https://doi.org/10.1063/1.532856

M. Havl´ıˇcek, A. U. Klimyk, S. Poˇsta. Representations of the q-deformed algebra Uq(iso2). Journal of Physics A: Mathematical and General 32(25):4681, 1999. https://doi.org/10.1088/0305-4470/32/25/310

M. Havl´ıˇcek, S. Poˇsta, A. U. Klimyk. Representations of the q-deformed algebra soq(2, 1). In Symmetry in Nonlinear Mathematical Physics, vol. 30 of Proceedings of Institute of Mathematics of NAS of Ukraine, pp. 280–287. 2000.

M. Havl´ıˇcek, A. U. Klimyk, S. Poˇsta. Central elements of the algebras U′ q (som) and Uq(isom). Czechoslovak Journal of Physics 50(1):79–84, 2000. https://doi.org/10.1023/A:1022825031633

M. Havl´ıˇcek, A. U. Klimyk, S. Poˇsta. Classification of representations of the algebra Uq′(so3) through examples. Czechoslovak Journal of Physics 50(11):1235–1238, 2000. https://doi.org/10.1023/A:1022804806462

M. Havl´ıˇcek, S. Poˇsta, A. U. Klimyk. Some basic properties of nonstandard deformations U′ q(so3), U′ q(so4). In S. T. Ali, H.-D. Doebner, M. Keyl, R. Werner (eds.), Trends in Quantum Mechanics: Proceedings of the International Symposium Goslar, Germany, pp. 10–17. 1999.

M. Havl´ıˇcek, S. Poˇsta. On the classification of irreducible finite-dimensional representations of U′ q(so3) algebra. Journal of Mathematical Physics 42(1):472–500, 2001. https://doi.org/10.1063/1.1328078

M. Havl´ıˇcek, A. U. Klimyk, S. Poˇsta. Representations of the q-deformed algebra U′ q (so4). Journal of Mathematical Physics 42(11):5389–5416, 2001. https://doi.org/10.1063/1.1402631

M. Havl´ıˇcek, S. Poˇsta, A. U. Klimyk. Classification of representations of the algebra Uq′(so3) through examples II. Physics of Atomic Nuclei 64(12):2151–2155, 2001. https://doi.org/10.1134/1.1432917

ˇC. Burd´ık, M. Havl´ıˇcek, O. Navr´atil, S. Poˇsta. Ideals of the enveloping algebra U(osp(1, 2)). Journal of Generalized Lie Theory and Applications 2(3):132–136, 2008.

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M. Havl´ıˇcek, J. Patera, E. Pelantov´a. On the maximal Abelian subgroups of the diagonalizable automorphisms of simple classical Lie algebras. In H. D. Doebner, P. Nattermann, W. Scherer (eds.), Group Theoretical Methods in Physics, Proceedings of XXI International Colloquium on Group Theoretical Methods in Physics, pp. 116–120. World Scientific, Singapore, 1997.

M. Havl´ıˇcek, J. Patera, E. Pelantov´a. On the fine gradings of simple classical Lie algebras. International Journal of Modern Physics A 12(1):189–194, 1997. https://doi.org/10.1142/S0217751X97000268

M. Havl´ıcek, J. Patera, E. Pelantova. On Lie gradings II. Linear Algebra and its Applications 277(1–3):97–125, 1998. https://doi.org/10.1016/S0024-3795(97)10039-8

M. Havl´ıˇcek, J. Patera, E. Pelantov´a. On Lie gradings III. Gradings of the real forms of classical Lie algebras. Linear Algebra and its Applications 314(1–3):1–47, 2000. https://doi.org/10.1016/S0024-3795(00)00099-9

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M. Havl´ıˇcek, J. Patera, E. Pelantov´a, J. Tolar. Automorphisms of the fine grading of sl(n,C) associated with the generalized Pauli matrices. Journal of Mathematical Physics 43(2):1083–1094, 2002. https://doi.org/10.1063/1.1430046

M. Havl´ıˇcek, E. Pelantov´a, J. Patera, J. Tolar. Distinguished bases of sl(n,C) and their symmetries. In Quantum Theory and Symmetries, pp. 366–370. World Scientific, 2002. https://doi.org/10.1142/9789812777850_0043

M. Havl´ıˇcek, J. Patera, E. Pelantov´a, J. Tolar. On Pauli graded contractions of sl(3,C). Journal of Nonlinear Mathematical Physics 11(1):37–42, 2004. https://doi.org/10.2991/jnmp.2004.11.s1.4

M. Havl´ıˇcek, E. Pelantov´a, J. Tolar. On representations of sl(n,C) compatible with a Z2-grading. Acta Polytechnica 50(5):30–39, 2010. https://doi.org/10.14311/1261

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M. Havl´ıˇcek, J. Kotrbat´y, P. Moylan, S. Poˇsta. Construction of representations of Poincar´e group using Lie fields. Journal of Mathematical Physics 59(2):021702, 2018. https://doi.org/10.1063/1.4993153

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J. Blank, P. Exner, M. Havl´ıˇcek. Hilbert space operators in quantum physics. College Park, MD: American Institute of Physics, 1994.

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Published

2025-11-07

How to Cite

Campoamor-Stursberg, R. (2025). The scientific legacy of Miloslav Havlíček. Acta Polytechnica, 65(5), 500-514. https://doi.org/10.14311/AP.2025.65.0500