共查询到20条相似文献,搜索用时 15 毫秒
1.
M. Mahdavi-Hezavehi J.-P. Tignol 《Proceedings of the American Mathematical Society》2003,131(12):3673-3676
Let be a division algebra of prime degree . A set of criteria is given for cyclicity of in terms of subgroups of the multiplicative group of . It is essentially shown that is cyclic if and only if contains a nonabelian metabelian subgroup.
2.
We develop necessary and sufficient conditions for central simple algebras to have involutions of the first kind, and to be
tensor products of quaternion subalgebras. The theory is then applied to give an example of a division algebra of degree 8
with involution (of the first kind), without quaternion subalgebras, answering an old question of Albert; another example
is a division algebra of degree 4 with involution (*) has no (*)-invariant quaternion subalgebras.
The research of the second author is supported by the Anshel Pfeffer Chair.
The third author would like to express his gratitude to Professor J. Tits for many stimulating conversations. 相似文献
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S. V. Pchelintsev 《Siberian Mathematical Journal》2007,48(6):1060-1073
We prove that every exceptional prime alternative algebra satisfies the Engel identity [[x, y], y] = 0 of index 2. 相似文献
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An example is given of division algebrasD
1 andD
2 of odd prime degreep over a fieldK such thatD
1 andD
2 have no common subfield properly containingF, butD
1
⊗i
⊗
K
D
2 is not a division algebra for 1≤i≤p−1.
Supported in part by the NSF. 相似文献
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Letk be any field andG a finite group. Given a cohomology class α∈H
2(G,k
*), whereG acts trivially onk
*, one constructs the twisted group algebrak
αG. Unlike the group algebrakG, the twisted group algebra may be a division algebra (e.g. symbol algebras, whereG⋞Z
n×Zn). This paper has two main results: First we prove that ifD=k
α
G is a division algebra central overk (equivalentyD has a projectivek-basis) thenG is nilpotent andG’ the commutator subgroup ofG, is cyclic. Next we show that unless char(k)=0 and
, the division algebraD=k
α
G is a product of cyclic algebras. Furthermore, ifD
p is ap-primary factor ofD, thenD
p is a product of cyclic algebras where all but possibly one are symbol algebras. If char(k)=0 and
, the same result holds forD
p, p odd. Ifp=2 we show thatD
2 is a product of quaternion algebras with (possibly) a crossed product algebra (L/k,β), Gal(L/k)⋞Z
2×Z2n. 相似文献
11.
Tomasz Maszczyk 《Monatshefte für Mathematik》2011,164(2):183-199
To any integral algebra with valuation an abelian group is associated, which measures how much the uniqueness of the division with remainder is violated. The analogy with the divisor class group is discussed. Examples of such groups are computed in cases of formal local rings of some cusps on an algebraic curve. 相似文献
12.
Tomasz Maszczyk 《Monatshefte für Mathematik》2011,96(1):183-199
To any integral algebra with valuation an abelian group is associated, which measures how much the uniqueness of the division
with remainder is violated. The analogy with the divisor class group is discussed. Examples of such groups are computed in
cases of formal local rings of some cusps on an algebraic curve. 相似文献
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Leo Marcus 《Israel Journal of Mathematics》1972,11(2):180-183
We show the existence of a prime minimal model containing an infinite set of indiscernibles. We then find a sentence ofL
ω1ω which is categorical in ω1 but whose model of power ω1 is not (ω1,L
ω1ω-homogeneous. This answers a question posed by Keisler. 相似文献
16.
From the viewpoint of higher dimensional Auslander–Reiten theory, we introduce a new class of finite dimensional algebras of global dimension n, which we call n-representation infinite. They are a certain analog of representation infinite hereditary algebras, and we study three important classes of modules: n-preprojective, n-preinjective and n -regular modules. We observe that their homological behaviour is quite interesting. For instance they provide first examples of algebras having infinite Ext1-orthogonal families of modules. Moreover we give general constructions of n-representation infinite algebras. 相似文献
17.
Pavel Etingof 《Journal of Pure and Applied Algebra》2006,205(2):310-322
Let p be a prime, and let RG(p) denote the set of equivalence classes of radically graded finite dimensional quasi-Hopf algebras over C, whose radical has codimension p. The purpose of this paper is to classify finite dimensional quasi-Hopf algebras A whose radical is a quasi-Hopf ideal and has codimension p; that is, A with gr(A) in RG(p), where gr(A) is the associated graded algebra taken with respect to the radical filtration on A. The main result of this paper is the following theorem: Let A be a finite dimensional quasi-Hopf algebra whose radical is a quasi-Hopf ideal of prime codimension p. Then either A is twist equivalent to a Hopf algebra, or it is twist equivalent to H(2), H±(p), A(q), or H(32), constructed in [5] and [8]. Note that any finite tensor category whose simple objects are invertible and form a group of order p under tensor is the representation category of a quasi-Hopf algebra A as above. Thus this paper provides a classification of such categories. 相似文献
18.
The embedding of certain infinite dimensional Lie algebras in generalized Clifford algobras C(N, p) is given. The correspondence between C(N,2) andgl(N, C) asN⇌∞ is pointed out. 相似文献
19.
Let A be a finite dimensional, basic and connected algebra (associative, with 1) over an algebraically closed field k. Denote by e1,...,en a complete set of primitive orthogonal idempotents in A and by Ai= A/AeiA. A is called a minimal algebra of infinite representation type provided A is itself of infinite representation type,whereas all Ai, 1≤i≤n,are of finite representation type. The main result gives the classification of the minimal algebras having a preprojective component in their Auslander-Reiten quiver. The classification is obtained by realizing that these algebras are essentially given by preprojective tilting modules over tame hereditary algebras. 相似文献
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