Crystallographic actions on Lie groups and post-Lie algebra structures
Communications in Mathematics (2021)
- Issue: 1, page 67-89
- ISSN: 1804-1388
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topBurde, Dietrich. "Crystallographic actions on Lie groups and post-Lie algebra structures." Communications in Mathematics (2021): 67-89. <http://eudml.org/doc/298279>.
@article{Burde2021,
abstract = {This survey on crystallographic groups, geometric structures on Lie groups and associated algebraic structures is based on a lecture given in the Ostrava research seminar in $2017$.},
author = {Burde, Dietrich},
journal = {Communications in Mathematics},
keywords = {Crystallographic groups; Pre-Lie algebras; Post-Lie algebras},
language = {eng},
number = {1},
pages = {67-89},
publisher = {University of Ostrava},
title = {Crystallographic actions on Lie groups and post-Lie algebra structures},
url = {http://eudml.org/doc/298279},
year = {2021},
}
TY - JOUR
AU - Burde, Dietrich
TI - Crystallographic actions on Lie groups and post-Lie algebra structures
JO - Communications in Mathematics
PY - 2021
PB - University of Ostrava
IS - 1
SP - 67
EP - 89
AB - This survey on crystallographic groups, geometric structures on Lie groups and associated algebraic structures is based on a lecture given in the Ostrava research seminar in $2017$.
LA - eng
KW - Crystallographic groups; Pre-Lie algebras; Post-Lie algebras
UR - http://eudml.org/doc/298279
ER -
References
top- Abels, H., Margulis, G. A., Soifer, G. A., 10.1016/S0764-4442(99)80356-5, C. R. Acad. Sci. Paris, 324, 253-258, (253) MR1438395DOI10.1016/S0764-4442(99)80356-5
- Abels, H., Margulis, G. A., Soifer, G. A., 10.1007/BF02775430, Israel J. Math., 148, 2005, 11-21, (2005) MR2191222DOI10.1007/BF02775430
- Auslander, L., 10.1016/0040-9383(64)90012-6, Topology, 3, 1964, 131-139, (1964) MR0161255DOI10.1016/0040-9383(64)90012-6
- Auslander, L., 10.1090/S0002-9939-1965-0185012-7, Proceedings of the American Mathematical Society, 16, 6, 1965, 1230-1236, (1965) MR0185012DOI10.1090/S0002-9939-1965-0185012-7
- Auslander, L., 10.2307/2373867, Amer. J. Math., 99, 4, 1977, 809-826, (1977) MR0447470DOI10.2307/2373867
- Baues, O., 10.1090/S0002-9947-99-02315-6, Trans. Amer. Math. Soc., 351, 7, 1999, 2979-2996, (1999) MR1608273DOI10.1090/S0002-9947-99-02315-6
- Benkart, G., Kostrikin, A., Kuznetsov, M., 10.1006/jabr.1995.1041, J. Algebra, 171, 3, 1995, 894-916, (1995) MR1315926DOI10.1006/jabr.1995.1041
- Benzécri, J. P., Variétés localement affines, Thèse, Princeton Univ. , Princeton, N. J., 1955, (1955) MR2612352
- Bieberbach, L., 10.1007/BF01564500, Math. Ann., 70, 3, 1911, 297-336, (1911) MR1511623DOI10.1007/BF01564500
- Bieberbach, L., 10.1007/BF01456724, Math. Ann., 72, 3, 1912, 400-412, (1912) MR1511704DOI10.1007/BF01456724
- Benoist, Y., Une nilvariété non affine, J. Diff. Geom., 41, 1995, 21-52, (1995) MR1316552
- Brown, H., Bülow, R., Neubüser, J., Wondratschek, H., Zassenhaus, H., Crystallographic groups of four-dimensional space, 1978, Wiley Monographs in Crystallography, Wiley-Interscience, New York-Chichester-Brisbane, (1978) MR0484179
- Burde, D., 10.1006/jabr.1994.1275, Journal of Algebra, 169, 1, 1994, 112-138, (1994) MR1296585DOI10.1006/jabr.1994.1275
- Burde, D., Grunewald, F., 10.1016/0022-4049(94)00002-Z, Journal of Pure and Applied Algebra, 99, 3, 1995, 239-254, (1995) MR1332900DOI10.1016/0022-4049(94)00002-Z
- Burde, D., 10.1006/jabr.1996.0151, Journal of Algebra, 181, 3, 1996, 884-902, (1996) MR1386584DOI10.1006/jabr.1996.0151
- Burde, D., 10.1142/S0129167X96000323, International Journal of Mathematics, 7, 5, 1996, 599-616, (1996) MR1411303DOI10.1142/S0129167X96000323
- Burde, D., 10.1007/s000130050173, Archiv der Mathematik, 70, 2, 1998, 118-127, (1998) MR1491457DOI10.1007/s000130050173
- Burde, D., Dekimpe, K., Deschamps, S., 10.1007/s00208-004-0623-1, Mathematische Annalen, 332, 1, 2005, 161-176, (2005) MR2139256DOI10.1007/s00208-004-0623-1
- Burde, D., 10.2478/s11533-006-0014-9, Central European Journal of Mathematics, 4, 3, 2006, 323-357, (2006) MR2233854DOI10.2478/s11533-006-0014-9
- Burde, D., Deschamps, K. Dekimpe and S., 10.1090/conm/491/09612, Contemporary Mathematics, 491, 2009, 125-140, (2009) MR2537054DOI10.1090/conm/491/09612
- Burde, D., Eick, B., Graaf, W. A. de, 10.1016/j.jalgebra.2009.04.041, Journal of Algebra, 22, 3, 2009, 602-612, (2009) MR2531213DOI10.1016/j.jalgebra.2009.04.041
- Burde, D., Dekimpe, K., Vercammen, K., 10.1515/jgt.2010.018, Journal of Group Theory, 13, 5, 2010, 703-719, (2010) MR2720199DOI10.1515/jgt.2010.018
- Burde, D., Moens, W. A., 10.1016/j.jalgebra.2010.09.028, Journal of Algebra, 325, 1, 2011, 440-460, (2011) MR2745549DOI10.1016/j.jalgebra.2010.09.028
- Burde, D., Vercammen, K. Dekimpe and K., 10.1016/j.laa.2012.04.007, Linear Algebra and its Applications, 437, 5, 2012, 1250-1263, (2012) MR2942346DOI10.1016/j.laa.2012.04.007
- Burde, D., Dekimpe, K., 10.17323/1609-4514-2013-13-1-1-18, Moscow Mathematical Journal, 13, 1, 2013, 1-18, (2013) MR3112213DOI10.17323/1609-4514-2013-13-1-1-18
- Burde, D., Dekimpe, K., 10.1016/j.jalgebra.2016.05.026, Journal of Algebra, 464, 2016, 226-245, (2016) MR3533429DOI10.1016/j.jalgebra.2016.05.026
- Burde, D., Moens, W. A., 10.1016/j.jalgebra.2016.07.030, Journal of Algebra, 467, 2016, 183-201, (2016) MR3545958DOI10.1016/j.jalgebra.2016.07.030
- Burde, D., Globke, W., 10.1016/j.jalgebra.2017.06.009, Journal of Algebra, 487, 2017, 200-216, (2017) MR3671190DOI10.1016/j.jalgebra.2017.06.009
- Burde, D., Globke, W., Minchenko, A., 10.1007/s00031-018-9483-8, Transformation Groups, 24, 3, 2019, 769-780, (2019) MR3989690DOI10.1007/s00031-018-9483-8
- Burde, D., Dekimpe, K., Moens, W. A., 10.1016/j.jalgebra.2019.02.003, Journal of Algebra, 526, 2019, 12-29, (2019) MR3914193DOI10.1016/j.jalgebra.2019.02.003
- Burde, D., Ender, C., Moens, W. A., 10.1142/S0218196718500406, International Journal of Algebra and Computation, 28, 5, 2018, 915-933, (2018) MR3844707DOI10.1142/S0218196718500406
- Burde, D., Gubarev, V., 10.1080/00927872.2018.1536206, Communications in Algebra, 47, 5, 2019, 2280-2296, (2019) MR3977738DOI10.1080/00927872.2018.1536206
- Burde, D., Zusmanovich, P., 10.1080/00927872.2019.1612426, Communications in Algebra, 47, 12, 2019, 5218-5226, (2019) MR4019336DOI10.1080/00927872.2019.1612426
- Burde, D., Ender, C., 10.1016/j.laa.2019.09.010, Linear Algebra and its Applications, 584, 2020, 107-126, (2020) MR4009591DOI10.1016/j.laa.2019.09.010
- Burde, D., Gubarev, V., 10.1142/S0218196720500071, International Journal of Algebra and Computation, 30, 3, 2020, 451-466, (2020) MR4082417DOI10.1142/S0218196720500071
- Buser, P., A geometric proof of Bieberbach's theorems on crystallographic groups, Enseign. Math., 31, 1-2, 1985, 137-145, (1985) MR0798909
- Dekimpe, K., Igodt, P., 10.1007/s002220050160, Invent. Math., 129, 1, 1997, 121-140, (1997) MR1464868DOI10.1007/s002220050160
- Dekimpe, K., 10.1016/S0040-9383(02)00030-7, Topology, 42, 4, 2003, 821-832, (2003) MR1958530DOI10.1016/S0040-9383(02)00030-7
- Ender, C., Post-Lie algebra structures on classes of Lie algebras, PhD-thesis, University of Vienna, 2019, (2019)
- Fried, D., Goldman, W., 10.1016/0001-8708(83)90053-1, Adv. Math., 47, 1983, 1-49, (1983) MR0689763DOI10.1016/0001-8708(83)90053-1
- Goldman, W. M., Two papers which changed my life: Milnor's seminal work on flat manifolds and bundles, Frontiers in complex dynamics, Princeton Math. Ser., 51, 2014, 679-703, (2014) MR3289925
- Gromov, M., Piatetski-Shapiro, I., 10.1007/BF02698928, Inst. Hautes Études Sci. Publ. Math., 66, 1988, 93-103, (1988) MR0932135DOI10.1007/BF02698928
- Helmstetter, J., 10.5802/aif.764, Ann. Inst. Fourier, 29, 1979, 17-35, (1979) MR0558586DOI10.5802/aif.764
- Hilbert, D., 10.1090/S0002-9904-1902-00923-3, Bulletin of the AMS, 87, 10, 1902, 437-479, (1902) MR1557926DOI10.1090/S0002-9904-1902-00923-3
- Jacobson, N., 10.1090/S0002-9939-1955-0068532-9, Proc. Am. Math. Soc., 6, 1955, 281-283, (1955) MR0068532DOI10.1090/S0002-9939-1955-0068532-9
- Margulis, G.A., 10.1007/BF01104978, J. Soviet Math., 36, 1987, 129-139, (1987) DOI10.1007/BF01104978
- Milnor, J., 10.1016/0001-8708(77)90004-4, Advances in Math., 25, 1977, 178-187, (1977) MR0454886DOI10.1016/0001-8708(77)90004-4
- Plesken, W., Schulz, T., 10.1080/10586458.2000.10504417, Experiment. Math., 9, 3, 2000, 407-411, (2000) MR1795312DOI10.1080/10586458.2000.10504417
- Schwarzenberger, R.L.E., 10.1017/S0305004100048696, Proc. Cambridge Philos. Soc., 76, 1974, 23-32, (1974) MR0349867DOI10.1017/S0305004100048696
- Segal, D., 10.1007/BF01444735, Math. Ann., 293, 1992, 569-578, (1992) MR1170527DOI10.1007/BF01444735
- Thurston, W.P., Three-dimensional geometry and topology. Vol. 1, 35, 1997, Edited by Silvio Levy. Princeton Mathematical Series, Princeton University Press, Princeton, NJ, (1997) MR1435975
- Tomanov, G., Properly discontinuous group actions on affine homogeneous spaces (English summary) Reprinted in Proc. Steklov Inst. Math., Algebra, Geometriya i Teoriya Chisel, 292, 1, 2016, 268-279, (2016) MR3628466
- Vallette, B., 10.1016/j.jpaa.2006.03.012, J. Pure and Applied Algebra, 208, 2, 2007, 699-725, (2007) MR2277706DOI10.1016/j.jpaa.2006.03.012
- (ed.), E. B. Vinberg, Geometry II, 29, 1991, Encyclopedia of Mathematical Sciences, Springer Verlag, (1991)
- Zassenhaus, H., 10.1007/BF02568029, Comment. Math. Helv., 21, 1948, 117-141, (1948) MR0024424DOI10.1007/BF02568029
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