We determined the inner products of two conformal vectors with central charge 1 2 whose τ -involutions generates S3 if none of τ -involutions are trivial. We also see that a subVA generated by such conformal vectors is a VOA with central charge 1 2 + 20 21 or 4 5 + 6 7 and has a Griess algebra of dimension three or four, respectively.

An involution or anti-involution is a self-inverse linear mapping. In this paper, we will present two real quaternion matrices, one corresponding to a real quaternion involution and one corresponding to a real quaternion anti-involution. Moreover, properties and geometrical meanings of these matrices will be given as reflections in R^3.

We study the maps induced on cohomology by a Nikulin (i.e. a symplectic) involution on a K3 surface. We parametrize the eleven dimensional irreducible components of the moduli space of algebraic K3 surfaces with a Nikulin involution and we give examples of the general K3 surface in various components. We conclude with some remarks on MorrisonNikulin involutions, these are Nikulin involutions wh...

Let In be the class of all signed involutions in the hyperoctahedral group Bn and let In(T ) be the set of involutions in In which avoid a set T of signed patterns. In this paper, we complete a further case of the program initiated by Simion and Schmidt [6] by enumerating In(T ) for all signed permutations T ⊆ B2.

We consider in this work the enumeration of involutions by descent sets, and based on that, by descent numbers. Formulas of the number of involutions with a prescribed descent set, with a prescribed descent number and Frobenius-type formulas are given.

In this paper, we study the essential dimension of classes of central simple algebras with involutions of index less or equal to 4. Using structural theorems for simple algebras with involutions, we obtain the essential dimension of projective and symplectic groups of small degree.

We show that there are exactly nine distinct PL involutions on the nonorientable 2-sphere bundle over Sl, up to PL equivalences. This, together with results of [1], [3] and [8], classifies all PL involutions on the 2sphere bundles over S1.

Lie algebra involutions and their fixed-point subalgebras give rise to symmetric spaces real forms of complex algebras, are well-studied in the context symmetrizable Kac-Moody algebras. In this paper we study a generalization. Namely, introduce concept pseudo-involution, an automorphism which is only required act involutively on stable Cartan subalgebra, pseudo-fixed-point natural substitute fo...