Involutions and Anticommutativity in Group Rings

Canadian mathematical bulletin

Edgar G. Goodaire²  César Polcino Milies¹ 

[1] Instituto de Matemática e Estatística, Universidade de São Paulo, Caixa Postal 66.281, CEP 05314-970, São Paulo SP, Brasil;Memorial University of Newfoundland, St. John's, NF, A1C 5S7

关键词: $C^*$-algebra;    tracial approximation;    $K_0$-monoid;   

DOI  :  10.4153/CMB-2011-178-2

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

Let $gmapsto g^*$ denote an involution on agroup $G$. For any (commutative, associative) ring$R$ (with $1$), $*$ extends linearly to an involutionof the group ring $RG$. An element $alphain RG$is symmetric if $alpha^*=alpha$ andskew-symmetric if $alpha^*=-alpha$.The skew-symmetric elements are closed underthe Lie bracket, $[alpha,eta]=alphaeta-etaalpha$.In this paper, we investigate when this set is also closedunder the ring product in $RG$.The symmetric elements are closed under the Jordanproduct, $alphacirceta=alphaeta+etaalpha$.Here, we determine when this product is trivial.These two problemsare analogues of problems about the skew-symmetric andsymmetric elements in group rings that have received alot of attention.

【 授权许可】

Unknown