منابع مشابه
Fixed Points of Involutive Automorphisms of the Bruhat Order
Applying a classical theorem of Smith, we show that the poset property of being Gorenstein∗ over Z2 is inherited by the subposet of fixed points under an involutive poset automorphism. As an application, we prove that every interval in the Bruhat order on (twisted) involutions in an arbitrary Coxeter group has this property, and we find the rank function. This implies results conjectured by F. ...
متن کاملOn Involutive Anti-Automorphisms of Finite Abelian Groups
We investigate various aspects of involutions of groups, i.e, anti-automorphisms of order at most two. The emphasis is on finite abelian groups. We count the number of involutions for the cyclic groups, and consider the problem for direct products of groups. We also give a characterization for the set of skewed squares of finitely generated abelian groups with identity as the involution. The pr...
متن کاملAn Instruction Sequence Semigroup with Involutive Anti-Automorphisms
We introduce an algebra of instruction sequences by presenting a semigroup C in which programs can be represented without directional bias: in terms of the next instruction to be executed, C has both forward and backward instructions and a C-expression can be interpreted starting from any instruction. We provide equations for thread extraction, i.e., C’s program semantics. Then we consider thre...
متن کاملAutomorphisms, Root Systems, and Compactifications of Homogeneous Varieties
Let G be a complex semisimple group and let H ⊆ G be the group of fixed points of an involutive automorphism of G. Then X = G/H is called a symmetric variety. In [CP], De Concini and Procesi have constructed an equivariant compactification X which has a number of remarkable properties, some of them being: i) The boundary is the union of divisors D1, . . . , Dr. ii) There are exactly 2 orbits. T...
متن کاملComprehensive Involutive Systems
In this paper we consider parametric ideals and introduce a notion of comprehensive involutive system. This notion plays the same role in theory of involutive bases as the notion of comprehensive Gröbner system in theory of Gröbner bases. Given a parametric ideal, the space of parameters is decomposed into a finite set of cells. Each cell yields the corresponding involutive basis of the ideal f...
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ژورنال
عنوان ژورنال: Journal of the Mathematical Society of Japan
سال: 1984
ISSN: 0025-5645
DOI: 10.2969/jmsj/03640643