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A Chevalley involution C of a connected reductive group G satisfies C(h) = h−1 for all h in some Cartan subgroup of G. Furthermore, C takes any semisimple1 element to a conjugate of its inverse....
A Franklin Type Involution for Squares
Franklin type involution Ramanujan's partial theta identity Andrews' identity
2014/6/3
We find an involution as a combinatorial proof of a Ramanujan's partial theta identity. Based on this involution, we obtain a Franklin type involution for squares in the sense that the classical Frank...
Decomposition of spinor groups by the involution σ' in exceptional Lie groups
Decomposition of spinor groups involution σ' in exceptional Lie groups
2011/2/22
The compact exceptional Lie groups F4,E6,E7 and E8 have spinor groups as a subgroup as follows.
Generating the Mobius group with involution conjugacy classes
Mobius group involution conjugacy classes
2011/2/28
A k-involution is an involution with a fixed point set of codimension k. The conjugacy class of such an involution, denoted Sk, generates M¨ob(n)-the the group of isometries of hyperbolic n-space-if k...
An Involution for the Gauss Identity
involution Ferrers diagrams Gauss identity Gauss coefficients Schur function plethysm
2014/6/3
We obtain an involution for a classical identity of Guass on the alternating sum of the Gauss coefficients. It turns out that the refinement of our involution with restrictions on the heights of Ferre...
Adjacency Preserving Bijection Maps of Hermitian Matrices over any Division Ring with an Involution
division ring with involution hermitian matrix adjacency geometry of matrices
2007/12/11
Let $D$ be any division ring with an involution, ${\mathscr H}_n(D)$ be the space of all $n\times n$ hermitian matrices over $D$. Two hermitian matrices $A$ and $B$ are said to be adjacent if ${\rm ra...
p -Banach algebras with generalized involution and C*-algebra structure
p-Banach algebras generalized involution involutive anti-morphism C*-algebra
2010/3/1
In this paper, we consider p-Banach algebras endowed with a generalized involution. We show that various C*-like conditions force the algebra to be C*-algebra under an equivalent norm.