共查询到20条相似文献,搜索用时 19 毫秒
1.
Alexander Merkurjev 《K-Theory》2006,37(3):311-319
We prove that the reduced Whitehead group SK
1(A) is generically nontrival for any central simple algebra A of index divisible by 4.
This work has been supported by the NSF grant DMS #0355166. 相似文献
2.
Mehran Motiee 《manuscripta mathematica》2013,141(3-4):717-726
We completely determine all torsion abelian groups that can occur as the torsion subgroup of the Whitehead group of a division algebra of prime index. More precisely, we prove that if D is a division algebra of prime index, then the torsion subgroup of K 1(D) is locally cyclic. Conversely, if A is a torsion locally cyclic group, then there exists a division algebra D of prime index such that the torsion subgroup of K 1(D) is isomorphic to A. Our result can be considered as a non-commutative version of May’s Theorem. 相似文献
3.
Roozbeh Hazrat 《Mathematische Zeitschrift》2010,264(2):295-299
Let A be an Azumaya algebra of constant rank n
2 over a Hensel pair (R, I) where R is a semilocal ring with n invertible in R. Then the reduced Whitehead group SK1(A) coincides with its reduction SK1(A/I A). This generalizes a result of Hazrat (J Algebra 305:687–703, 2006) to non-local Henselian rings. 相似文献
4.
For an Azumaya algebra A with center C of rank n
2 and a unitary involution τ, we study the stability of the unitary SK1 under reduction. We show that if R = C
τ is a Henselian ring with maximal ideal
\mathfrakm{\mathfrak{m}} and 2 and n are invertible in R then
SK1(A, t) @ SK1(A/ \mathfrakm A, overline t){{{\rm SK}_1}(A, \tau) \cong {{\rm SK}_1}(A/ \mathfrak{m} A, overline \tau)}. 相似文献
5.
Tim Wouters 《Algebras and Representation Theory》2013,16(3):729-745
In this text, we compare an invariant of the reduced Whitehead group SK 1 of a central simple algebra recently introduced by Kahn (2010) to other invariants of SK 1. Doing so, we prove the non-triviality of Kahn’s invariant using the non-triviality of an invariant introduced by Suslin (1991) which is non-trivial for Platonov’s examples of non-trivial SK 1 (Platonov, Math USSR Izv 10(2):211–243, 1976). We also give a formula for the value on the centre of the tensor product of two symbol algebras which generalises a formula of Merkurjev for biquaternion algebras (Merkurjev 1995). 相似文献
6.
Leonid N. Vaserstein 《代数通讯》2013,41(3):611-656
For any ring A, the group K1A is filtered by the Whitehead determinants of invertible matrices over A of different sizes. We want to compute the corresponding graded group (especially the highest degree non-zero term) in terms of symbols which generalize Mennicke’s symbol. In particular, we generalize the Bass-Milnor-Serre result which presents SK1A of a Dedekind ring A via the Mennicke symbol, to an arbitrary commutative ring A satisfying the Bass second stable range condition. As an application, SK1 is computed for some rings of continuous functions. Some of our theorems are partially known, but we have often weakened hypotheses, using stable range conditions rather than Krull dimension (having in mind applications to rings of continuous functions). 相似文献
7.
Mikhail Ershov 《Israel Journal of Mathematics》2007,158(1):297-347
Let D be a finite dimensional division algebra over a local field of characteristic p and let SL
1(D) denote the group of elements of reduced norm 1 in D. In this paper we prove that SL
1(D) is finitely presented as a profinite group.
This work is part of the author’s Ph.D. Thesis at Yale University. 相似文献
8.
A. R. Wadsworth 《manuscripta mathematica》2012,139(3-4):343-389
We prove formulas for SK1(E, τ), which is the unitary SK1 for a graded division algebra E finite-dimensional and semiramified over its center T with respect to a unitary involution τ on E. Every such formula yields a corresponding formula for SK1(D, ρ) where D is a division algebra tame and semiramified over a Henselian valued field and ρ is a unitary involution on D. For example, it is shown that if ${\sf{E} \sim \sf{I}_0 \otimes_{\sf{T}_0}\sf{N}}$ where I 0 is a central simple T 0-algebra split by N 0 and N is decomposably semiramified with ${\sf{N}_0 \cong L_1\otimes_{\sf{T}_0} L_2}$ with L 1, L 2 fields each cyclic Galois over T 0, then $${\rm SK}_1(\sf{E}, \tau) \,\cong\ {\rm Br}(({L_1}\otimes_{\sf{T}_0} {L_2})/\sf{T}_0;\sf{T}_0^\tau)\big/ \left[{\rm Br}({L_1}/\sf{T}_0;\sf{T}_0^\tau)\cdot {\rm Br}({L_2}/\sf{T}_0;\sf{T}_0^\tau) \cdot \langle[\sf{I}_0]\rangle\right].$$ 相似文献
9.
Irina Sviridova 《代数通讯》2013,41(9):3462-3490
We consider associative PI-algebras over an algebraically closed field of zero characteristic graded by a finite abelian group G. It is proved that in this case the ideal of graded identities of a G-graded finitely generated PI-algebra coincides with the ideal of graded identities of some finite dimensional G-graded algebra. This implies that the ideal of G-graded identities of any (not necessary finitely generated) G-graded PI-algebra coincides with the ideal of G-graded identities of the Grassmann envelope of a finite dimensional (G × ?2)-graded algebra, and is finitely generated as GT-ideal. Similar results take place for ideals of identities with automorphisms. 相似文献
10.
Let G be a compact abelian group. It is known that the second conjugate space L1**(G) of the group algebra L1(G) is a noneommutative, nonsemisimple, Banach algebra. It is not known if L1**(G) admits an involution. If it does, we show that it is P-coimnutative, and hence enjoys many of the properties of commutative Banach algebras. 相似文献
11.
Charles Lanski 《代数通讯》2013,41(5):1427-1446
ABSTRACT Let D be a division algebra with center F. Consider the group CK 1(D) = D*/F*D′ where D* is the group of invertible elements of D and D′ is its commutator subgroup. In this note we shall show that, assuming a division algebra D is a product of cyclic algebras, the group CK 1(D) is trivial if and only if D is an ordinary quaternion algebra over a real Pythagorean field F. We also characterize the cyclic central simple algebras with trivial CK 1 and show that CK 1 is not trivial for division algebras of index 4. Using valuation theory, the group CK 1(D) is computed for some valued division algebras. 相似文献
12.
HeJiwei 《高校应用数学学报(英文版)》2004,19(1):27-36
The axioms of A∞-algebras can be written as Maurer-Cartan equation. Infinitesimal multiplication of a graded associative algebra is defined and the integrability of infinitesimal multiplication is discussed through the Massey F-product. 相似文献
13.
Mohamed Lamei El-Mallah 《Journal of Algebra》1983,80(2):314-322
Let A denote a prehilbert absolute valued real algebra such that (x, x, x) = 0 for all x ε A; for this algebra we obtain the same results we have previously obtained for the flexible absolute valued algebra. Our main theorem is: A has a finite dimension 1, 2, 4 or 8, and is isotopic to
or C. One of the results concerning the isomorphism between A and
, C*,
or C shows that if for every two idempotents e1 and e2 in
, then A is isomorphic to
, C*,
or C. The example of infinite dimensional Hilbert absolute valued algebra given by Urbanik and Wright indicates that the assumption, (x, x, x) = 0 for all x ε A, is essential. 相似文献
14.
Let G be an abelian group, B the G-graded λ-Hopf algebra with A being a bicharacter on G. By introducing some new twisted algebras (coalgebras), we investigate the basic properties of the graded antipode and the structure for B. We also prove that a G-graded λ-Hopf algebra can be embedded in a usual Hopf algebra. As an application, it is given that if G is a finite abelian group then the graded antipode of a finite dimensional G-graded A-Hopf algebra is invertible. 相似文献
15.
We introduce the class of operators on Banach spaces having property (H) and study Weyl’s theorems, and related results for operators which satisfy this property. We show that a- Weyl’s theorem holds for every decomposable operator having property (H). We also show that a-Weyl’s theorem holds for every multiplier T of a commutative semi-simple regular Tauberian Banach algebra. In particular every convolution operator Tμ of a group algebra L1(G), G a locally compact abelian group, satisfies a-Weyl’s theorem. Similar results are given for multipliers of other important commutative Banach algebras. 相似文献
16.
Saharon Shelah 《Israel Journal of Mathematics》1975,21(4):319-349
We prove, in an axiomatic way, a compactness theorem for singular cardinals. We apply it to prove that, for singular λ, every λ-free algebra is free; and similar compactness results for transversals and colouring numbers. For the general result on free algebras, we develop some filters onS k(A). As an application we conclude thatV=L implies that every Whitehead group is free. 相似文献
17.
The aim of this paper is to study the graded limits of minimal affinizations over the quantum loop algebra of type G 2. We show that the graded limits are isomorphic to multiple generalizations of Demazure modules, and obtain defining relations of them. As an application, we obtain a polyhedral multiplicity formula for the decomposition of minimal affinizations of type G 2 as a \(U_{q}(\mathfrak {g})\)-module, by showing the corresponding formula for the graded limits. As another application, we prove a character formula of the least affinizations of generic parabolic Verma modules of type G 2 conjectured by Mukhin and Young. 相似文献
18.
Given a graded ample Hausdorff groupoid, we realise its graded Steinberg algebra as a partial skew inverse semigroup ring. We use this to show that for a partial action of a discrete group on a locally compact Hausdorff topological space which is totally disconnected, the Steinberg algebra of the associated groupoid is graded isomorphic to the corresponding partial skew group ring. We show that there is a one-to-one correspondence between the open invariant subsets of the topological space and the graded ideals of the partial skew group ring. We also consider the algebraic version of the partial -algebra of an abelian group and realise it as a partial skew group ring via a partial action of the group on a topological space. Applications to the theory of Leavitt path algebras are given. 相似文献
19.
Let R be a group graded ring . The map ( , ): R × R →1 defined by: (x,y) = (xy)1 , is an inner product on R. In this paper we investigate aspects of nondegeneracy of the product, which is a generalization of the notion of strongly G —graded rings,introduced by Dade. We show that various chain conditions are satisfied by R if and only if they are satisfied by R1 , and that when R1 is simple artinian, then R is a crossed product R1 * G. We give conditions for simple R-modules to be completely reducible R1 -modules . Finally, we prove an incomparability theorem,when G is finite abelian. 相似文献
20.
N. G. Khisamiev 《Siberian Mathematical Journal》2009,50(1):181-187
We consider a torsion-free nilpotent R p -group, the p-rank of whose quotient by the commutant is equal to 1 and either the rank of the center by the commutant is infinite or the rank of the group by the commutant is finite. We prove that the group is constructivizable if and only if it is isomorphic to the central extension of some divisible torsion-free constructive abelian group by some torsion-free constructive abelian R p -group with a computably enumerable basis and a computable system of commutators. We obtain similar criteria for groups of that type as well as divisible groups to be positively defined. We also obtain sufficient conditions for the constructivizability of positively defined groups. 相似文献