A formula is given for the discriminant of the tensor product of the canonical involution on a quaternion algebra and an orthogonal involution on a central simple algebra of degree divisible by 4. As an application, an alternative proof of Shapiro’s “Pfister Factor Conjecture” is given for tensor products of at most five quaternion algebras. Throughout this paper, the characteristic of the base...

This article establishes a few sufficient conditions of the forward-order law for core inverse elements in rings with involution. It also presents weighted and triple inverse. Additionally, we discuss hybrid involving different generalized inverses like Moore–Penrose inverse, group

‎let $r$ be a ring with involution $*$‎. ‎an additive mapping $t:rto r$ is called a left(respectively right) centralizer if $t(xy)=t(x)y$ (respectively $t(xy)=xt(y)$) for all $x,yin r$‎. ‎the purpose of this paper is to examine the commutativity of prime rings with involution satisfying certain identities involving left centralizers.

If ∗ : G → G is an involution on the finite group G, then ∗ extends to an involution on the integral group ring Z[G]. In this paper, we consider whether bicyclic units u ∈ Z[G] exist with the property that the group 〈u, u∗〉, generated by u and u∗, is free on the two generators. If this occurs, we say that (u, u∗) is a free bicyclic pair. It turns out that the existence of u depends strongly upo...

We will drop the compactness hypothesis on G in the results of §6, doing this in such a way that problems can be reduced to the compact case. This involves the notions of reductive Lie groups and algebras and Cartan involutions. Let © be a Lie algebra. A subalgebra S c © is called a reductive subaU gebra if the representation ad%\® of ίΐ on © is fully reducible. © is called reductive if it is a...

The Mullineux involution is a relevant map that appears in the study of modular representations symmetric group and alternating group. fixed points this are certain partitions particular interest. It known cardinality set these self-Mullineux equal to distinguished subset self-conjugate partitions. In work, we give an explicit bijection between two families terms symbol.

Let F be a non-Archimedean locally compact field with residual characteristic p, let G be an inner form of GLn(F), n 1 and let R be an algebraically closed field of characteristic different from p. When R has characteristic > 0, the image of an irreducible smooth R-representation π of G by the Aubert involution need not be irreducible. We prove that this image (in the Grothendieck group of G) c...

Let g be a complex semisimple Lie algebra. In this paper, we prove that the action of a certain involution on canonical bases for irreducible g-modules deened by Lusztig agrees with the action of a special element of the associated simply connected Lie group, up to a scalar of unit absolute value. This leads to formulas for the number of xed points of the involution by means of the Weyl charact...