DECOMPOSITION OF MATRICES INTO COMMUTATORS OF REFLECTIONS
DECOMPOSITION OF MATRICES INTO COMMUTATORS OF REFLECTIONS
摘要
Let F be a field and let resA = rank(A - I) for any A in GLnF. We prove that every matrix in SLnF is a product of at most [resA/2] + 2 commutators of reflections for n 】 2 except for n - 2 and F = F2.
基金
This research is supported by the National Natural Science Foundation of China.
参考文献11
-
1E. Cartan, Lecons sur la Theorie des Spineurs, Hermann, Paris, 1938.
-
2J. Dieudonne, Sur les Groups Classiques, Hermann, Paris, 1948.
-
3P. Scherk, On the decomposition of orthogonalities into symmetries, Proc. Amer. Math. Soc.,1950, 1: 481-491.
-
4H. Radjavi, Decomposition of matrices into simple involutions, Lift. Algebra and Appl., 1975, 12:247-255.
-
5D. Djokovic and J. Malzan, Products of reflections in the general linear group over a division ring,Lin. Algebra and Appl., 1979, 28: 53-62.
-
6K. Shoda, uber den Kommutator der Matrizen, J. Math. Soc. Japan, 1951, 3 : 78-81.
-
7R. Thompson, Commutaors in the special and general linear groups, Trans. Amer. Math. Soc.,1961, 101: 16-33.
-
8A. Hahn, The elements of the orthogonal group as products of commutators of symmetries, J. of Algebra, 1996, 184: 927-944.
-
9F. Knuppel, Products of simple isometries of given conjugacy types, Forum Math., 1993, 5: 441-458.
-
10H. You and J. Z. Lan, Decomposition of matrices into 2-involutions, Lin. Algebra and Appl., 1993,186: 235-253.
-
1皇甫明,梁波.域上特殊线性群的伸缩换位子的刻画[J].大连交通大学学报,2009,30(3):101-104.
-
2游宏,郑宝东.表特殊线性群中元素为平延换位子之积(英文)[J].数学进展,2001,30(2):133-140. 被引量:4
-
3南基洙,张永正.局部环上SL_n(R)的元素的2对合分解[J].东北师大学报(自然科学版),1996,28(1):17-22.
-
4生玉秋,王路群.域上的辛平延的换位子[J].黑龙江大学自然科学学报,2003,20(1):8-13. 被引量:2
-
5苏开乐.Some semantic results about the operator in Levesque's logic of belief[J].Chinese Science Bulletin,1996,41(12):1053-1054.