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排序方式: 共有190条查询结果,搜索用时 437 毫秒
1.
Onofrio Mario Di Vincenzo Plamen Koshlukov Roberto La Scala 《Advances in Applied Mathematics》2006,37(4):541
In this paper we describe completely the involutions of the first kind of the algebra UTn(F) of n×n upper triangular matrices. Every such involution can be extended uniquely to an involution on the full matrix algebra. We describe the equivalence classes of involutions on the upper triangular matrices. There are two distinct classes for UTn(F) when n is even and a single class in the odd case.Furthermore we consider the algebra UT2(F) of the 2×2 upper triangular matrices over an infinite field F of characteristic different from 2. For every involution *, we describe the *-polynomial identities for this algebra. We exhibit bases of the corresponding ideals of identities with involution, and compute the Hilbert (or Poincaré) series and the codimension sequences of the respective relatively free algebras.Then we consider the *-polynomial identities for the algebra UT3(F) over a field of characteristic zero. We describe a finite generating set of the ideal of *-identities for this algebra. These generators are quite a few, and their degrees are relatively large. It seems to us that the problem of describing the *-identities for the algebra UTn(F) of the n×n upper triangular matrices may be much more complicated than in the case of ordinary polynomial identities. 相似文献
2.
John Kalliongis Darryl McCullough 《Transactions of the American Mathematical Society》1996,348(5):1739-1755
The observation that the quotient orbifold of an orientation- reversing involution on a 3-dimensional handlebody has the structure of a compression body leads to a strong classification theorem, and general structure theorems. The structure theorems decompose the action along invariant discs into actions on handlebodies which preserve the -fibers of some -bundle structure. As applications, various results of R. Nelson are proved without restrictive hypotheses.
3.
We study complex Lagrangian submanifolds of a compact hyper-Kähler manifold and prove two results: (a) that an involution of a hyper-Kähler manifold which is antiholomorphic with respect to one complex structure and which acts non-trivially on the corresponding symplectic form always has a fixed point locus which is complex Lagrangian with respect to one of the other complex structures, and (b) there exist Lagrangian submanifolds which are complex with respect to one complex structure and are not the fixed point locus of any involution which is anti-holomorphic with respect to one of the other complex structures. 相似文献
4.
5.
Let R be a ring with involution *. We consider R as a ring equipped with a new product r s = rs + sr*. The relationship between (ordinary) ideals of R and right ideals of R with respect to the product is studied.AMS Subject Classification (2000): 16W10, 16D25 相似文献
6.
Let X be a closed, oriented Riemannian 4-manifold. Suppose that a cyclic group Z(
p
(p is prime) acts on X by an orientation preserving isometry with an embedded Riemann surface as fixed point set. We study the representation of Z
p
on the Spinc-bundles and the Z
p-invariant moduli space of the solutions of the Seiberg–Witten equations for a Spinc-structure X. When the Z
p
action on the determinant bundle det L acts non-trivially on the restriction L| over the fixed point set , we consider -twisted solutions of the Seiberg-Witten equations over a Spinc-structure ' on the quotient manifold X/Z
p
X', (0,1). We relate the Z
p
-invariant moduli space for the Spinc-structure on X and the -twisted moduli space for the Spinc-structure on X'. From this we induce a one-to-one correspondence between these moduli spaces and calculate the dimension of the -twisted moduli space. When Z
p
acts trivially on L|, we prove that there is a one-to-one correspondence between the Z
p
-invariant moduli space M(
Zp
and the moduli space M (") where ' is a Spinc-structure on X' associated to the quotient bundle L/Z
p
X'. vskip0pt When p = 2, we apply the above constructions to a Kahler surface X with b
2
+
(X) > 3 and H
2(X;Z) has no 2-torsion on which an anti-holomorphic involution acts with fixed point set , a Lagrangian surface with genus greater than 0 and []2H
2(H ;Z). If
K
X
2 > 0 or K
X
2
= 0 and the genus g()> 1, we have a vanishing theorem for Seiberg–Witten invariant of the quotient manifold X'. When K
X
2
= 0 and the genus g()= 1, if there is a Z
2-equivariant Spinc-structure on X whose virtual dimension of the Seiberg–Witten moduli space is zero then there is a Spinc-structure " on X' such that the Seiberg-Witten invariant is ±1. 相似文献
7.
LetD be a division ring which possesses an involution a → α . Assume that
is a proper subfield ofD and is contained in the center ofD. It is pointed out that ifD is of characteristic not two, D is either a separable quadratic extension of F or a division ring of generalized quaternions
over F and that if D is of characteristic two,D is a separable quadratic extension ofF. Thus the trace map Tr:D → F, a → a + a is always surjective, which is formerly posed as an assumption in the fundamental theorem of n×n hermitian
matrices overD when n ≥ 3 and now can be deleted. WhenD is a field, the fundamental theorem of 2 × 2 hermitian matrices overD has already been proved. This paper proves the fundamental theorem of 2×2 hermitian matrices over any division ring of generalized
quaternions of characteristic not two
This research was completed during a visit to the Academy of Mathematics and System Sciences, Chinese Academy of Sciences. 相似文献
8.
A proper subgroup H of a group G is said to be strongly embedded if 2 (H) and 2(HH
g) (for all
). An involution i of G is said to be finite if
(for all g G). As is known, the structure of a (locally) finite group possessing a strongly embedded subgroup is determined by the theorems of Burnside and Brauer--Suzuki, provided that the Sylow 2-subgroup contains a unique involution. In this paper, sufficient conditions for the equality m
2(G)= 1 are established, and two analogs of the Burnside and Brauer—Suzuki theorems for infinite groups G possessing a strongly embedded subgroup and a finite involution are given. 相似文献
9.
The construction of the sum of a direct (semilattice ordered) system of algebras introduced by J. Plonka – later known as the Plonka sum – is one of the most important methods of composition in universal algebra, having a number of applications in different algebraic theories, such as semigroup theory, semiring theory, etc. In this paper we present a more general way for constructing algebras with involution, that is, algebraic systems equipped with a unary involutorial operation which is at the same time an antiautomorphism of the underlying algebra. It is the sum – involutorial Plonka sum, as we call it – of an involution semilattice ordered system of algebras. We investigate its basic properties, as well as the problem of its subdirect decomposition. 相似文献
10.
Jan M. Aarts Robbert J. Fokkink 《Proceedings of the American Mathematical Society》2001,129(9):2803-2807
There is a close relation between the color number of a continuous map without fixed points and the topological dimension. If is an involution, the color number is also related to the co-index. An addition theorem for the color number is established thus underscoring the interrelations between color number, dimension and co-index.