Normal forms for matrices over uniserial rings of length two
This paper develops methods to describe the conjugacy classes of GL(n,R) on Rn×n for a serial ring R of length two. The main result is a reduction to a computation in the matrix algebra over the residue class field of R, which in some cases can be done theoretically without any actual computation.
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| Published in | Journal of algebra Vol. 358; pp. 250 - 256 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Inc
15.05.2012
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| Abstract | This paper develops methods to describe the conjugacy classes of GL(n,R) on Rn×n for a serial ring R of length two. The main result is a reduction to a computation in the matrix algebra over the residue class field of R, which in some cases can be done theoretically without any actual computation. |
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| AbstractList | This paper develops methods to describe the conjugacy classes of GL(n,R) on Rn×n for a serial ring R of length two. The main result is a reduction to a computation in the matrix algebra over the residue class field of R, which in some cases can be done theoretically without any actual computation. |
| Author | Jambor, Sebastian Plesken, Wilhelm |
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| Cites_doi | 10.1016/j.jalgebra.2010.05.024 10.1016/0024-3795(83)90204-5 10.1007/BF01351597 10.1080/00927870902747266 10.1090/S0002-9939-1973-0309963-X |
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| Keywords | Conjugacy classes Normal forms of matrices |
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| References | Cohn (br0050) 1982 Jambor (br0090) 2011 Pomfret (br0130) 1973; 37 The GAP Group, GAP – Groups, Algorithms, and Programming, Version 4.4.12, 2008. Singla (br0140) 2010; 324 Huppert (br0070) 1967; Band 134 Nechaev (br0100) 1983 Appelgate, Onishi (br0020) 1983; 87 Avni, Onn, Prasad, Vaserstein (br0030) 2009; 37 Betten, Braun, Fripertinger, Kerber, Kohnert, Wassermann (br0040) 2006; vol. 18 Pizarro (br0120) 1983; 54 Albert (br0010) 1961; vol. XXIV Nobs (br0110) 1977; 229 Jacobson (br0080) 1980 Betten (10.1016/j.jalgebra.2012.01.028_br0040) 2006; vol. 18 Pomfret (10.1016/j.jalgebra.2012.01.028_br0130) 1973; 37 Cohn (10.1016/j.jalgebra.2012.01.028_br0050) 1982 Huppert (10.1016/j.jalgebra.2012.01.028_br0070) 1967; Band 134 Appelgate (10.1016/j.jalgebra.2012.01.028_br0020) 1983; 87 10.1016/j.jalgebra.2012.01.028_br0060 Singla (10.1016/j.jalgebra.2012.01.028_br0140) 2010; 324 Jacobson (10.1016/j.jalgebra.2012.01.028_br0080) 1980 Jambor (10.1016/j.jalgebra.2012.01.028_br0090) Nobs (10.1016/j.jalgebra.2012.01.028_br0110) 1977; 229 Pizarro (10.1016/j.jalgebra.2012.01.028_br0120) 1983; 54 Avni (10.1016/j.jalgebra.2012.01.028_br0030) 2009; 37 Albert (10.1016/j.jalgebra.2012.01.028_br0010) 1961; vol. XXIV Nechaev (10.1016/j.jalgebra.2012.01.028_br0100) 1983 |
| References_xml | – year: 1980 ident: br0080 article-title: Basic Algebra. II contributor: fullname: Jacobson – volume: vol. 18 year: 2006 ident: br0040 article-title: Error-Correcting Linear Codes publication-title: Algorithms Comput. Math. contributor: fullname: Wassermann – volume: Band 134 year: 1967 ident: br0070 article-title: Endliche Gruppen. I publication-title: Grundlehren Math. Wiss. contributor: fullname: Huppert – volume: 324 start-page: 2543 year: 2010 end-page: 2563 ident: br0140 article-title: On representations of general linear groups over principal ideal local rings of length two publication-title: J. Algebra contributor: fullname: Singla – year: 2011 ident: br0090 article-title: Source files contributor: fullname: Jambor – volume: 54 start-page: 29 year: 1983 end-page: 51 ident: br0120 article-title: Similarity classes of publication-title: Linear Algebra Appl. contributor: fullname: Pizarro – volume: 37 start-page: 421 year: 1973 end-page: 422 ident: br0130 article-title: Similarity of matrices over finite rings publication-title: Proc. Amer. Math. Soc. contributor: fullname: Pomfret – start-page: 81 year: 1983 end-page: 101 ident: br0100 article-title: Similarity of matrices over a commutative local Artinian ring publication-title: Tr. Semin. im. I. G. Petrovskogo contributor: fullname: Nechaev – year: 1982 ident: br0050 article-title: Algebra, vol. 1 contributor: fullname: Cohn – volume: 37 start-page: 2601 year: 2009 end-page: 2615 ident: br0030 article-title: Similarity classes of publication-title: Comm. Algebra contributor: fullname: Vaserstein – volume: 229 start-page: 113 year: 1977 end-page: 133 ident: br0110 article-title: Die irreduziblen Darstellungen von publication-title: Math. Ann. contributor: fullname: Nobs – volume: vol. XXIV year: 1961 ident: br0010 article-title: Structure of Algebras publication-title: Amer. Math. Soc. Colloq. Publ. contributor: fullname: Albert – volume: 87 start-page: 233 year: 1983 end-page: 238 ident: br0020 article-title: Similarity problem over publication-title: Proc. Amer. Math. Soc. contributor: fullname: Onishi – volume: Band 134 year: 1967 ident: 10.1016/j.jalgebra.2012.01.028_br0070 article-title: Endliche Gruppen. I contributor: fullname: Huppert – volume: vol. 18 year: 2006 ident: 10.1016/j.jalgebra.2012.01.028_br0040 article-title: Error-Correcting Linear Codes contributor: fullname: Betten – volume: 324 start-page: 2543 issue: 9 year: 2010 ident: 10.1016/j.jalgebra.2012.01.028_br0140 article-title: On representations of general linear groups over principal ideal local rings of length two publication-title: J. Algebra doi: 10.1016/j.jalgebra.2010.05.024 contributor: fullname: Singla – year: 1980 ident: 10.1016/j.jalgebra.2012.01.028_br0080 contributor: fullname: Jacobson – volume: 54 start-page: 29 year: 1983 ident: 10.1016/j.jalgebra.2012.01.028_br0120 article-title: Similarity classes of 3×3 matrices over a discrete valuation ring publication-title: Linear Algebra Appl. doi: 10.1016/0024-3795(83)90204-5 contributor: fullname: Pizarro – year: 1982 ident: 10.1016/j.jalgebra.2012.01.028_br0050 contributor: fullname: Cohn – volume: 229 start-page: 113 issue: 2 year: 1977 ident: 10.1016/j.jalgebra.2012.01.028_br0110 article-title: Die irreduziblen Darstellungen von GL2(Zp), insbesondere GL2(Z2) publication-title: Math. Ann. doi: 10.1007/BF01351597 contributor: fullname: Nobs – volume: 87 start-page: 233 issue: 2 year: 1983 ident: 10.1016/j.jalgebra.2012.01.028_br0020 article-title: Similarity problem over SL(n,Zp) publication-title: Proc. Amer. Math. Soc. contributor: fullname: Appelgate – volume: 37 start-page: 2601 issue: 8 year: 2009 ident: 10.1016/j.jalgebra.2012.01.028_br0030 article-title: Similarity classes of 3×3 matrices over a local principal ideal ring publication-title: Comm. Algebra doi: 10.1080/00927870902747266 contributor: fullname: Avni – start-page: 81 issue: 9 year: 1983 ident: 10.1016/j.jalgebra.2012.01.028_br0100 article-title: Similarity of matrices over a commutative local Artinian ring publication-title: Tr. Semin. im. I. G. Petrovskogo contributor: fullname: Nechaev – ident: 10.1016/j.jalgebra.2012.01.028_br0090 contributor: fullname: Jambor – volume: vol. XXIV year: 1961 ident: 10.1016/j.jalgebra.2012.01.028_br0010 article-title: Structure of Algebras contributor: fullname: Albert – volume: 37 start-page: 421 year: 1973 ident: 10.1016/j.jalgebra.2012.01.028_br0130 article-title: Similarity of matrices over finite rings publication-title: Proc. Amer. Math. Soc. doi: 10.1090/S0002-9939-1973-0309963-X contributor: fullname: Pomfret – ident: 10.1016/j.jalgebra.2012.01.028_br0060 |
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| Title | Normal forms for matrices over uniserial rings of length two |
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