291 research outputs found
Minimal algebras and 2-step nilpotent Lie algebras in dimension 7
No full textUsiamo i metodi di Bazzoni e Muñoz (Trans Am Math Soc 364:1007–1028, 2012) per ottenere una classificazione delle algebre minimali in dimensione 7, generate in grado 1, su un campo k di caratteristica char(k)≠2 , la cui filtrazione caratteristica ha lunghezza 2. In modo equivalente, classifichiamo algebre di Lie nilpotenti a 2 passi in dimensione 7. Tale classificazione recupera inoltre il tipo di omotopia reale delle 2-nilvarietà in dimensione 7.We use the methods of Bazzoni and Muñoz (Trans Am Math Soc 364:1007–1028, 2012) to give a classification of 7-dimensional minimal algebras, generated in degree 1, over any field k of characteristic char(k)≠2 , whose characteristic filtration has length 2. Equivalently, we classify 2-step nilpotent Lie algebras in dimension 7. This classification also recovers the real homotopy type of 7-dimensional 2-step nilmanifolds
Covering classes and 1-tilting cotorsion pairs over commutative rings
No full textWe are interested in characterising the commutative rings for which a 1-tilting cotorsion pair provides for covers, that is when the class A is a covering class. We use Hrbekšfs bijective correspondence between the 1-tilting cotorsion pairs over a commutative ring R and the faithful finitely generated Gabriel topologies on R. Moreover, we use results of Bazzoni-Positselski, in particular a generalisation of Matlis equivalence and their characterisation of covering classes for 1-tilting cotorsion pairs arising from flat injective ring epimorphisms. Explicitly, if is the Gabriel topology associated to the 1-tilting cotorsion pair, and R is the ring of quotients with respect to, we show that if A is covering, then G is a perfect localisation (in Stenstromšfs sense [B. Stenstrom, Rings of Quotients, Springer, New York, 1975]) and the localisation R has projective dimension at most one as an R-module. Moreover, we show that is covering if and only if both the localisation RG and the quotient rings R/J are perfect rings for every J ∈. Rings satisfying the latter two conditions are called G-almost perfect
Vaisman nilmanifolds
No full textWe prove that if a compact nilmanifold Γ∖G is endowed with a Vaisman structure, then G is isomorphic to the Cartesian product of the Heisenberg group with R
Special Types of Locally Conformal Closed G<sub>2</sub>-Structures
No full textMotivated by known results in locally conformal symplectic geometry, we study different classes of G 2 -structures defined by a locally conformal closed 3-form. In particular, we provide a complete characterization of invariant exact locally conformal closed G 2 -structures on simply connected Lie groups, and we present examples of compact manifolds with different types of locally conformal closed G 2 -structures
MODULI SPACES OF (CO)CLOSED G2-STRUCTURES ON NILMANIFOLDS
No full textWe compute the dimensions of some moduli spaces of left-invariant closed and coclosed G(2)-structures on 7-dimensional nilmanifolds, showing that they are not related to the third Betti number. We also prove that, in contrast to the case of closed G(2)-structures, the group of automorphisms of a coclosed G(2)-structure is not necessarily abelian
Locally conformally symplectic and Kähler geometry
No full textThe goal of this note is to give an introduction to locally conformally symplectic and Kähler geometry. In particular, Sections 1 and 3 aim to provide the reader with enough mathematical background to appreciate this kind of geometry. The reference book for locally conformally Kähler geometry is "Locally conformal K"ahler Geometry" by Sorin Dragomir and Liviu Ornea. Many progresses in this field, however, were accomplished after the publication of this book, hence are not contained there. On the other hand, there is no book on locally conformally symplectic geometry and many recent advances lie scattered in the literature. Sections 2 and 4 would like to demonstrate how these geometries can be used to give precise mathematical formulations to ideas deeply rooted in classical and modern Physics
Reduction in time : kinaesthetic and traumatic experiences of the present in literary texts
No full textThe chapter explores the dimension of the living present as a form of temporal reduction, looking at its manifestation in literary texts. Bazzoni proposes here a focus on the living present as different from a still, eternal moment, and contrasts the experience of the living present with the reduction at play in trauma. Finally, the author discusses the affective, ethical, and political dimensions of the temporality of the living present as a site of subjectivation, which effects a counter-reduction of normative discourses
‐structures on nilmanifolds
No full textWe classify seven-dimensional nilpotent Lie groups, decomposable or of nilpotency step at most 4, endowed with left-invariant purely coclosed G(2)-structures. This is done by going through the list of all seven-dimensional nilpotent Lie algebras given by Gong, providing an example of a left-invariant 3-form phi which is a pure coclosed G(2)-structure (i.e., it satisfies d*phi=0, phi perpendicular to d phi=0) for those nilpotent Lie algebras that admit them; and by showing the impossibility of having a purely coclosed G(2)-structure for the rest of them
Toric actions and convexity in cosymplectic geometry
No full textWe prove a convexity theorem for Hamiltonian torus actions on compact cosymplectic manifolds. We show that compact toric cosymplectic manifolds are mapping tori of equivariant symplectomorphisms of toric symplectic manifolds
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