322,873 research outputs found
Flag-transitive hyperplane complements of classical generalized quadrangles
No full textLet H be a geometric hyperplane of a classical finite generalized quadrangle Q and let C = Q H be its complement in Q, viewed as a point-line geometry. We shall prove that C admits a flag-transitive automorphism group if and only if H spans a hyperplane of the projective space in which Q is naturally embedded (but with Q viewed as Q(4, q) when Q = W(q), q even). Furthermore, if Q is the dual of Ii(4, q(2)) and H, C are as above, then C is flag-transitive if and only if H = p(perpendicular to) for some point p of Q
Uniform hyperplanes of finite dual polar spaces of rank 3
No full textLet Delta be a finite thick dual polar space of rank 3. We say that a hyperplane H of Delta is locally singular (respectively, quadrangular or ovoidal) if H boolean AND Q is the perp of a point (resp. a subquadrangle or an ovoid) of Q for every quad Q of Delta. If H is locally singular, quadrangular, or ovoidal, then we say that H is uniform. It is known that if H is locally singular, then either H is the set of points at non-maximal distance from a given point of Delta or Delta is the dual of L(6, q) and H arises from the generalized hexagon H(q). In this paper we prove that only two examples exist for the locally quadrangular case, arising in L(6, 2) and H (5, 4), respectively. We fail to rule out the locally ovoidal case, but we obtain some partial results on it, which imply that, in this case, the geometry Delta H induced by Delta on the complement of H cannot be flag-transitive. As a bi-product, the hyperplanes H with Delta H flag-transitive are classified. (C) 2001 Academic Press
An infinite-dimensional 2-generated primitive axial algebra of Monster type
No full textRehren proved in Axial algebras. Ph.D. thesis, University of Birmingham (2015), Trans Am Math Soc 369:6953–6986 (2017) that a primitive 2-generated axial algebra of Monster type (,) over a field of characteristic other than 2, has dimension at most 8 if ∉{2,4} if α∉{2β,4β}. In this note, we show that Rehren’s bound does not hold in the case α=4β by providing an example (essentially the unique one) of an infinite-dimensional 2-generated primitive axial algebra of Monster type (2,1/2) over an arbitrary field
of characteristic other than 2 and 3. We further determine its group of automorphisms and describe some of its relevant features
Classification of certain types of tilde geometries
No full textWe show that a certain class of diagram geometries called tilde geometries of symplectic type is simply connected. Here we prove that the corresponding amalgam is uniquely determined. The result then follows from Ivanov and Shpectorov (Geom. Dedicata45 (1993), 1-23).</p
Geometries with bi-linear and bi-affine diagrams
No full textWe consider geometries belonging to the following diagram of rank n ≥ 4,. {A figure is presented}. We prove that when n ≥ 5, the only simply connected examples for this diagram arise from PG(n,q) by removing a hyperplane and the star of a point. We call these geometries bi-affine geometries. They are of two types, according to whether the point and the hyperplane chosen are incident or not. We also prove that there are just three types of flag-transitive simply connected examples for the rank 4 case of the above diagram, namely the two bi-affine geometries of rank 3 and the (well-known) two-sided extension of PG(2,4) for HS. © 1995
Diffusive author(s), cohesive author: Analysis of S/N (1994)
No full textThis study indicates the ways in which various aspects of the author(s) are brought forth in Dumb type’s performance art, the S/N production. Previous research has suggested a non-hierarchical organization of Dumb type and the absence of a “privileged author” in Dumb type’s collaborative work, S/N. However, the results that I have investigated from member’s interviews on the creative process of S/N along with my analysis of the recorded images of S/N, indicate a different aspect of the author(s). First, S/N was created through, so to speak, the collective ideas of the members of Dumb type. Further, S/N has at least nine quotations from previous performances, installations, and printed writings, besides the work-in-progress technique. Explicating one of the “author functions” as given by Michel Foucault, each text has plural subjects of the author. However, it has been revealed from members’ interviews that Teiji Furuhashi had a decision-making role in selecting the members’ ideas within the performance. Since then, S/N has had plural subjects of creation; however, Furuhashi is one of the subjects of creation along with the “privileged author.” S/N has plural authors (diffusive authors) yet at the same time, it has a “privileged author,” Teiji Furuhashi (cohesive author)
Odd-dimensional orthogonal groups as amalgams of unitary groups. Part 1: General simple connectedness
No full textAbstractWe extend the Phan theory described in [C. Bennett, R. Gramlich, C. Hoffman, S. Shpectorov, Curtis–Phan–Tits theory, in: A.A. Ivanov, M.W. Liebeck, J. Saxl (Eds.), Groups, Combinatorics, and Geometry, World Scientific, River Edge, 2003, pp. 13–29] to the last remaining infinite series of classical Chevalley groups over finite fields. Namely, we prove that the twin buildings for the group Spin(2n+1,q2), q odd, admit a unique unitary flip and that the corresponding flipflop geometry is simply connected for almost all finite fields Fq2. Applying standard methods from amalgam theory, this results in a characterization of central quotients of the group Spin(2n+1,q) by a Phan system of rank one and rank two subgroups. In the present first part of a series of two articles we present simple connectedness results for sufficiently large fields or sufficiently large rank. To be precise, the result stated in the present paper is proved for all cases but n=3 and q∈{3,5,7,9}, the remaining cases are dealt with in the sequel [R. Gramlich, M. Horn, W. Nickel, Odd-dimensional orthogonal groups as amalgams of unitary groups. Part 2: Machine computations, submitted for publication] computationally
Going Beyond Counting First Authors in Author Co-citation Analysis
No full textThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Solid subalgebras in algebras of Jordan type half
No full textThe class of algebras of Jordan type η was introduced by Hall, Rehren and Shpectorov in 2015 within the much broader class of axial algebras. Algebras of Jordan type are commutative algebras A over a field of characteristic not 2, generated by primitive idempotents, called axes, whose adjoint action on A has minimal polynomial dividing (x−1)x(x−η) and where multiplication of eigenvectors follows the rules similar to the Peirce decomposition in Jordan algebras.Naturally, Jordan algebras generated by primitive idempotents are examples of algebras of Jordan type η=12. Further examples are given by the Matsuo algebras constructed from 3-transposition groups. These examples exist for all values of η≠0,1. Jordan algebras and (factors of) Matsuo algebras constitute all currently known examples of algebras of Jordan type and it is conjectured that there are now additional examples.In this paper we introduce the concept of a solid 2-generated subalgebra, as a subalgebra J such that all primitive idempotents from J are axes of A. We prove that, for axes a,b∈A, if (a,b)∉{0,14,1} then J=⟨⟨a,b⟩⟩ is solid, that is, generic 2-generated subalgebras are solid. Furthermore, in characteristic zero, J is solid even for the values (a,b)=0,1. As a corollary, in characteristic zero, either A has infinitely many axes and an infinite automorphism group, or it is a Matsuo algebra or a factor of Matsuo algebra
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