Let G be a connected complex reductive algebraic groups. The dual group ~LG^0 of G is an algebraic group whose simple root system π~v is the dual of the simple root system π of G and whose characteristic lattice is ...Let G be a connected complex reductive algebraic groups. The dual group ~LG^0 of G is an algebraic group whose simple root system π~v is the dual of the simple root system π of G and whose characteristic lattice is just the dual lattice X_*(T) of the characteristic lattice X~*(T)of G, where T is a given maximal torus of G and the simple root system π corresponds to a Borel subgroup B containing T. For the detail of the definition of a dual group see Ref. [1].展开更多
A ring R is called orthogonal if for any two idempotents e and f in R, the condition that e and f are orthogonal in R implies the condition that [eR] and [fR] are orthogonal in K0(R)+, i.e., [eR]∧[fR] = 0. In this pa...A ring R is called orthogonal if for any two idempotents e and f in R, the condition that e and f are orthogonal in R implies the condition that [eR] and [fR] are orthogonal in K0(R)+, i.e., [eR]∧[fR] = 0. In this paper, we shall prove that the K0-group of every orthogonal, IBN2 exchange ring is always torsion-free, which generalizes the main result in [3].展开更多
基金Project supported in part by the National Natural Science Foundation of China and K. C. Wong Education Foundation.
文摘Let G be a connected complex reductive algebraic groups. The dual group ~LG^0 of G is an algebraic group whose simple root system π~v is the dual of the simple root system π of G and whose characteristic lattice is just the dual lattice X_*(T) of the characteristic lattice X~*(T)of G, where T is a given maximal torus of G and the simple root system π corresponds to a Borel subgroup B containing T. For the detail of the definition of a dual group see Ref. [1].
基金the National Natural Science Foundation of China （No. 10571080） the Natural Science Foundation of Jiangxi Province （No. 0611042） the Science and Technology Projiet Foundation of Jiangxi Province （No. G[20061194） and the Doctor Foundation of Jiangxi University of Science and Technology.
文摘A ring R is called orthogonal if for any two idempotents e and f in R, the condition that e and f are orthogonal in R implies the condition that [eR] and [fR] are orthogonal in K0(R)+, i.e., [eR]∧[fR] = 0. In this paper, we shall prove that the K0-group of every orthogonal, IBN2 exchange ring is always torsion-free, which generalizes the main result in [3].
