摘要:

For (A, σ) a central simple algebra of even degree with orthogonal involution, we present a method for constructing isotropic right ideals in the even Clifford algebra (C0(A, σ)σ) from isotropic right ideals in (A, σ). We then use this construction to fully describe the twisted flag varieties associated to algebraic groups of typeD4(including the trialitarian groups).

ISSN:0092-7872    

DOI:10.1080/00927879908826465

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879908826466

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879908826467

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor

摘要:

Let ĝ an untwisted affine Kac-Moody algebra over the field C, and letUq(ĝ) be the associated quantum enveloping algebra; letUq(ĝ) be the Lusztig’s integer form ofUq(ĝ), generated byq-divided powers of Chevalley generators over a suitable sub ringRofC(q). We prove a Poincaré-Birkhoff-Witt like theorem forUq(ĝ), yielding a basis overRmade of ordered products ofq-divided powers of suitable quantum root vectors.

ISSN:0092-7872    

DOI:10.1080/00927879908826468

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor

摘要:

Assume thatϕ(R, m, k) → (S, n, l) is a local homomorphism between commutative noetherian local ringsRandS. We say that anS-moduleMis almost finite overRif it is finitely generated overS(theR-structure onMis induced by ϕ). We investigate the homological behaviour of such modules, as well as various properties of the ringsRandSin the presence of an almost finite module of finite flat dimension overR.

ISSN:0092-7872    

DOI:10.1080/00927879908826469

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor

摘要:

Central simple triples are important for the classification of prime Jordan triples of Clifford type in arbitrary characterstics. For triples and pairs (or even for unital Jordan algebras of characteristic 2), there is no workable notion of center, and the concept of “central simple” system must be understood as “centroid-simple”. The centroid of a Jordan system (algebra, triple, or pair) consists of the “natural” scalars for that system: the largest unital, commutative ring Γ such that the system can be considered as a quadratic Jordan system over Γ. In this paper we will characterize the centroids of the basic simple Jordan algebras, triples, and pairs. (Consideration of the tangled ample outer ideals in Jordan algebras of quadratic forms will be left to a separate paper.) A powerful tool is the Eigenvalue Lemma, that a centroidal transformation on a prime system over φ which has an eigenvalue α in φ must actually be scalar multiplication by α. An important consequence is that a prime system over φ with reduced elementsPxJ= φx (or which grows reduced elements under controlled conditions) must already be central, Γ = φ.

ISSN:0092-7872    

DOI:10.1080/00927879908826470

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor

摘要:

somorphism problems for finite dimensional algebras can be computationally hard. When the algebras are monomial, it is shown, refining work of Shirayanagi, that there is a simple definitive combinatorial method. However, examples show that no such criterion is possible if the class of algebras is expanded to that of diagram algebras (in the sense of Fuller). The presentation of a diagram algebra is field independent but the existence of an isomorphism between two such is not. (Subject classes: 16G30, 16P10, 20M25).

ISSN:0092-7872    

DOI:10.1080/00927879908826471

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor

摘要:

We give the complete classification of ∑-pure-injective modules over a commutative Prüfer ring.

ISSN:0092-7872    

DOI:10.1080/00927879908826472

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879908826473

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879908826444

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor