Bass' nilpotent unitary $K_1$-group of unitary ring
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 32, Tome 460 (2017), pp. 134-157 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper we introduce and study Bass' nilpotent unitary $K_1$-group of the unitary ring. We obtain a set of the unitary representative of this group and describe all representative one by unitary unipotent matrix.
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V. I. Kopeiko. Bass' nilpotent unitary $K_1$-group of unitary ring. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 32, Tome 460 (2017), pp. 134-157. http://geodesic.mathdoc.fr/item/ZNSL_2017_460_a5/

[1] Kh. Bass, Algebraicheskaya $K$-teoriya, Mir, M., 1973 | MR | Zbl

[2] G. Cortinas, C. Haesemeyer, M. E. Walker, C. Weibel, “Bass' NK groups and cdh-fibrant Hochschild homology”, Invent. Math., 89 (2010), 421–448 | DOI | MR

[3] J. F. Davis, Some remarks on Nil groups in algebraic $K$-theory, Preprint, arXiv: 0803.1641v2[math.KT]

[4] H. Bass, “Some problems in “classical” algebraic $K$-theory”, Lect. Notes Math., 342, 1973, 3–73 | MR | Zbl

[5] S. E. Cappell, “Unitary nilpotent groups and hermitian $K$-theory”, Bull. AMS, 80 (1974), 1117–1122 | DOI | MR | Zbl

[6] F. T. Farrell, “The exponent of UNil”, Topology, 18 (1979), 305–312 | DOI | MR | Zbl

[7] F. Connolly, A. Ranicki, “On the calculation of UNil”, Adv. Math., 195 (2005), 205–258 | DOI | MR | Zbl

[8] V. I. Kopeiko, “O gomotopizatsii unitarnogo $K_1$-funktora”, Algebra i analiz, 20:5 (2008), 99–108 | MR | Zbl

[9] H. Bass, “Unitary algebraic $K$-theory”, Lect. Notes Math., 343, 1973, 57–265 | DOI | MR | Zbl

[10] A. J. Hahn, O. T. O'Meara, The classical groups and $K$-theory, Springer, Berlin et al., 1989 | MR | Zbl

[11] V. I. Kopeiko, “Transfer unitarnogo $K_1$-funktora pri polinomialnykh rasshireniyakh kolets”, Algebra i analiz, 29:3 (2017), 34–60 | MR

[12] L. N. Vasershtein, “Stabilizatsiya unitarnykh i ortogonalnykh grupp nad koltsami s involyutsiei”, Mat. sbornik, 81(123):3 (1970), 328–351 | MR | Zbl

[13] H. Bass, J. Milnor, J.-P. Serre, “Solution of the congruence subgroup problem for $SL_n (n\geq 3)$ and $Sp_{2n}(n\geq 2)$”, Inst. Hautes Études Sci. Publ. Math., 33 (1967), 59–133 ; Matem. (sb. perevodov), 14:6 (1970), 64–128 ; Matem. (sb. perevodov), 15:1 (1971), 44–60 | DOI | MR | Zbl | Zbl

[14] V. I. Kopeiko, “Stabilizatsiya simplekticheskikh grupp nad koltsom mnogochlenov”, Mat. sbornik, 106(148):1 (1978), 94–107 | MR | Zbl

[15] M. Karoubi, “Périodicité de la $K$-théorie hermitienne”, Lect. Notes Math., 343, 1973, 301–411 | DOI | MR | Zbl