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Crossed group rings with a finite set of degrees of indecomposable representations over Dedekind domains

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Słowa kluczowe
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Rocznik
Strony
771--782
Opis fizyczny
Bibliogr. 29 poz.
Twórcy
autor
  • Institute of Mathematics Pedagogical Academy Arciszewskiego 22b 76-200 Słupsk, Poland
autor
  • Institute of Mathematics Pedagogical Academy Arciszewskiego 22b 76-200 Słupsk, Poland
Bibliografia
  • [1] L. F. Barannyk and P. M. Gudivok, Projective representations of finite groups over number rings, Mat. Sbornik, 82 (124) (1970), 423-443=Math. USSR Sb., 11 (1970), 391-410.
  • [2] L. F. Barannyk and P. M. Gudivok, Crossed group rings of finite groups and rings of P-adic integers with finitely many indecomposable integral representations, Mat. Sbornik. 108(150)(1979), 187-211=Math. USSR., 36(1980), 173-194.
  • [3] S. D. Berman and P. M. Gudivok, Integral representations of finite groups, Dokl. Akad. Nauk SSSR, 145 (1962), 1199-1201=Soviet Math. Dokl., 3 (1962), 1172-1174.
  • [4] S. D. Berman and P. M. Gudivok, Indecomposable representations of finite groups over the ring of p-adic integers, Izv. Akad. Nauk SSSR, Ser. Mat. 28 (1964), 875-910, English transl., Amer. Math. Soc. Transl., (2) 50 (1966), 77-113.
  • [5] Z. I. Borevich and D. K. Faddeev, Theory of homology in groups, II. Vestnik Leningrad. Univ. 14 (1959), No 7, 72-87 (in Russian).
  • [6] S. B. Conlon, Twisted group algebras and their representations, J. Austral. Math. Soc. 4 (1964), 152-173.
  • [7] C. W. Curtis and I. Reiner, Representation Theory of Finite Groups and Associative Algebras, New York: Interscience, 1962; 2nd ed., 1966.
  • [8] C. W. Curtis and I. Reiner, Methods of Representation Theory, Vol. I, New York: Wiley, 1981.
  • [9] F. E. Diederichsen, Uber die Ausreduktion ganzzahliger Gruppendarstellungen bei arithmetischer Aquivalenz, Abh., Math. Sem. Univ. Hamburg, 14 (1940), 357-412.
  • [10] J. A. Drozd and V. V. Kirichenko, Finite Dimensional Algebras, Springer, Berlin, 1994.
  • [11] P. Gabriel and A. V. Roiter, Representations of Finite Dimensional Algebras. Algebra VIII, Encyclopedia of Math. Sc., Vol. 73, Springer, 1992; 2nd print., Springer, Berlin, 1997.
  • [12] P. M. Gudivok, Representations of finite groups over number rings, Izv. Akad. Nauk SSSR, Ser. Mat., 31 (1967), 799-834=Math. USSR Izv., 1(1967), 773-805.
  • [13] P. M. Gudivok, On boundedness of degrees of indecomposable modular representations of finite groups over principal ideal rings, Dopovidi Akad. Nauk USSR, Ser. A(1971), No 8, 683-685 (in Ukrainian).
  • [14] P. M. Gudivok, On the number of indecomposable integral p-adic representations of crossed group rings, Mat. Sb., 91(133) (1973), 27-49=Math. USSR Sb., 20 (1973).
  • [15] P. M. Gudivok, V. S. Drobotenko and A. I. Lichtman, On representations of finite groups over the ring of residue classes mod m, Ukrain. Math. J., 16 (1964), 82-89 (in Russian).
  • [16] P. M. Gudivok, V. M. Oros and A. V. Roiter, On representations of finite p-groups over a ring of formal power series with p-adic integer coefficients, Ukrain. Math. J. 44 (1992), No 6, 753-765 (in Russian).
  • [17] P. M. Gudivok and E. Ya. Pogorilyak, On modular representations of finite groups over integral domains, Proc. Steklov Inst. Math., No 4 (1991), 87-95.
  • [18] P. M. Gudivok and V. I. Pogorilyak, On indecomposable representations of finite p-groups over commutative local rings, Dopovidi Nat. Akad. Nauk Ukra'iny (1996), No 5, 7-11 (in Russian).
  • [19] A. Heller and I. Reiner, Representations of cyclic groups rings of integers I, Ann. Math., 76 (1962), 73-92.
  • [20] A. Heller and I. Reiner, Representations of cyclic groups rings of integers II, Ann. Math. 77 (1963), 318-328.
  • [21] D. G. Higman, Indecomposable representations at characteristic p, Duke Math. J. 21 (1954), 377-381.
  • [22] H. Jacobinski, Sur les ordres commutatifs avec un nombre fini de reseaux indecomposables, Acta Math. 118 (1967), 1-31.
  • [23] G. Karpilovsky, Group representations, North-Holland Mathematical Studies 177, 1993.
  • [24] L. A. Nazarova, Unimodular representations of the four group, Dokl. Akad. Nauk SSSR, 140 (1961), 1011-1014=Soviet Math. Dokl., 2 (1961), 1304-1307.
  • [25] J. Okninski, Semigroups of Matrices, Series in Algebra, Vol. 6, World Scientific, London, 1998.
  • [26] K. W. Roggenkamp, Gruppenringe von unendlichem Darstellungstyp, Mat. Z. 96 (1967), 393-398.
  • [27] A. V. Roiter, On representations of the cyclic group of fourth order by integral matrices, Vestnik Leningrad. Univ. 15 (1960), No 19, 65-74 (in Russian).
  • [28] A. H. Schofield, Representations of Rings over Skew Fields, London Math. Soc. Lecture Notes Series, No. 92 (Cambridge University Press, 1985).
  • [29] D. Simson, Linear Representations of Partially Ordered Sets and Vector Space Categories, Algebra, Logic and Applications, Vol. 4, Gordon & Breach Science Publishers, Switzerland-Australia, 1992.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-PWA1-0040-0020
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