Improved K₁-stability for the embedding D₅ into E₆

References

• Bak, A., Petrov, V. A., Tang, G. (2003). Stability for quadratic K1. K-Theory 30(1):1–11. DOI: 10.1023/B:KTHE.0000015340.00470.a9.
   Google Scholar
• Bak, A., Tang, G. (2000). Stability for hermitian K1. J. Pure Appl. Algebra 150(2):107–121. DOI: 10.1016/S0022-4049(99)00035-3.
   Web of Science ®Google Scholar
• Bass, H. (1964). K-theory and stable algebra. Publ. Math. l'IHÉS. 22(1):5–60. DOI: 10.1007/BF02684689.
   Google Scholar
• Bass, H. (1986). Algebraic K-Theory. New York: W. A. Benjamin, Inc.
   Google Scholar
• Bourbaki, N. (2004). Elements of mathematics. In Lie Groups and Lie Algebras. Chapters 7–9. Berlin: Springer.
   Google Scholar
• Bourbaki, N. (2008). Elements of mathematics. In Lie Groups and Lie Algebras. Chapters 4–6. Berlin: Springer-Verlag, p. 300.
   Google Scholar
• Chevalley, C. (1960). Certain schemas des groupes semi-simples. Sem. Bourbaki. 6:219–234.
   Google Scholar
• Estes, D., Ohm, J. (1967). Stable range in commutative rings. J. Algebra 7(3):343–362. DOI: 10.1016/0021-8693(67)90075-0.
   Web of Science ®Google Scholar
• Magurn, B. A., Van der Kallen, W., Vaserstein, L. N. (1988). Absolute stable rank and Witt cancellation for noncommutative rings. Invent. Math. 91(3):525–542. DOI: 10.1007/BF01388785.
   Web of Science ®Google Scholar
• Matsumoto, H. (1969). Sur les sous-groupes arithmétiques des groupes semisimples déployés. Ann. Sci. École Norm. Sup. 2(1):1–62. DOI: 10.24033/asens.1174.
   Google Scholar
• Plotkin, E. B. (1998). On the stability of the K1-functor for Chevalley groups of type E7. J. Algebra 210:67–85.
   Google Scholar
• Plotkin, E. B. (1991). Stability theorems for K1-functors for Chevalley groups. Proceedings of the Conference on Nonassociative Algebras and Related Topics, Hiroshima.
   Google Scholar
• Plotkin, E. B. (1993). Surjective stabilization for K1-functor for some exceptional Chevalley groups. J. Soviet Math. 64:751–767.
   Google Scholar
• Plotkin, E. B., Semenov, A. A., Vavilov, N. A. (1998). Visual basic representations: an atlas. Int. J. Algebra Comput. 08(01):61–95. DOI: 10.1142/S0218196798000053.
   Google Scholar
• Stavrova, A. K. (2020). Chevalley groups of polynomial rings over Dedekind domains. J. Group Theory 23(1):121–132. DOI: 10.1515/jgth-2019-0100.
   Web of Science ®Google Scholar
• Stein, M. R. (1971). Generators, relations, and coverings of Chevalley groups over commutative rings. Amer. J. Math. 93(4):965–1004. DOI: 10.2307/2373742.
   Web of Science ®Google Scholar
• Stein, M. R. (1971). Relativizing functors on rings and algebraic K-theory. J. Algebra 19(1):140–152. DOI: 10.1016/0021-8693(71)90123-2.
   Web of Science ®Google Scholar
• Stein, M. R. (1978). Stability theorems for K1, K2 and related functors modeled on Chevalley groups. Jpn. J. Math. 4(1):77–108. DOI: 10.4099/math1924.4.77.
   Google Scholar
• Stein, M. R. (1983). Matsumoto’s solution of the congruence subgroup problem and stability theorems in algebraic K-theory. Proceedings of the 19th Meeting Algebra Section Math. Soc., University of Tokyo, Japan, pp. 32–44.
   Google Scholar
• Steinberg, R. G. (1985). Some consequences of the elementary relations in SLn. Contemp. Math. 45:335–350.
   Google Scholar
• Stepanov, A. V. (2013). Elementary calculus in Chevalley groups over rings. J. Prime Res. Math. 9:79–95.
   Google Scholar
• Suslin, A. A., Tulenbaev, M. S. (1981). Stabilization theorem for the Milnor K2-functor. J. Math. Sci. 17(2):1804–1819. DOI: 10.1007/BF01091768.
   Google Scholar
• Taddei, G. (1986). Normalité des groupes élémentaire dans les groupes de Chevalley sur un anneau. Contemp. Math. 55:693–710.
   Google Scholar
• Tits, J. (1976). Systemes générateurs de groupes de congruences. C. R. Acad. Sci. Paris Sér. A. 283:693–695.
   Google Scholar
• Vaserstein, L. N. (1969). On the stabilization of the general linear group over a ring. Sb. Math. 8(3):383–400.
   Google Scholar
• Vaserstein, L. N. (1970). Stabilization of unitary and orthogonal groups over a ring with involution. Sb. Math. 10(3):307–326.
   Google Scholar
• Vaserstein, L. N. (1986). On normal subgroups of Chevalley groups over commutative rings. Tohoku Math. J. 38(2):219–230. DOI: 10.2748/tmj/1178228489.
   Web of Science ®Google Scholar
• Vaseršteĭn, L. N., Suslin, A. A. (1976). Serre’s problem on projective modules over polynomial rings, and algebraic K-theory. Math. Ussr. Izv. 10(5):937–1001. DOI: 10.1070/IM1976v010n05ABEH001822.
   Web of Science ®Google Scholar
• Vavilov, N. A. (2000). A third look at weight diagrams. Rend. Semin. Mat. Univ. Padova. 104:201–250.
   Google Scholar
• Vavilov, N. A. (2008). Can one see the signs of structure constants? St. Petersburg Math. J. 19(4):519–543. DOI: 10.1090/S1061-0022-08-01008-X.
   Web of Science ®Google Scholar