1,721,545 research outputs found
A new species of Branchinecta (Crustacea: Anostraca) from Brasil
No full textRogers, Christopher, Ferreira, Aloisio (2007): A new species of Branchinecta (Crustacea: Anostraca) from Brasil. Zootaxa 1445: 27-34, DOI: 10.5281/zenodo.17610
On the homotopy theory for Lie ∞–groupoids, with an application to integrating L∞–algebras
No full text2-PLECTIC GEOMETRY, COURANT ALGEBROIDS, AND CATEGORIFIED PREQUANTIZATION
No full textA 2-plectic manifold is a manifold equipped with a closed nondegenerate 3-form, just as a symplectic manifold is equipped with a closed nondegenerate 2-form. In 2-plectic geometry one finds the higher analogues of many structures familiar from symplectic geometry. For example, any 2-plectic manifold has a Lie 2-algebra consisting of smooth functions and Hamiltonian 1-forms. This is equipped with a Poisson-like bracket which only satisfies the Jacobi identity up to "coherent chain homotopy". Over any 2-plectic manifold is a vector bundle equipped with extra structure called an exact Courant algebroid. This Courant algebroid is the 2-plectic analogue of a transitive Lie algebroid over a symplectic manifold. Its space of global sections also forms a Lie 2-algebra. We show that this Lie 2-algebra contains an important sub-Lie 2-algebra which is isomorphic to the Lie 2-algebra of Hamiltonian 1-forms. Furthermore, we prove that it is quasi-isomorphic to a central extension of the (trivial) Lie 2-algebra of Hamiltonian vector fields, and therefore is the higher analogue of the well-known Kostant-Souriau central extension in symplectic geometry. We interpret all of these results within the context of a categorified prequantization procedure for 2-plectic manifolds. In doing so, we describe how U(1)-gerbes, equipped with a connection and curving, and Courant algebroids are the 2-plectic analogues of principal U(1) bundles equipped with a connection and their associated Atiyah Lie algebroids
2-PLECTIC GEOMETRY, COURANT ALGEBROIDS, AND CATEGORIFIED PREQUANTIZATION
No full textA 2-plectic manifold is a manifold equipped with a closed nondegenerate 3-form, just as a symplectic manifold is equipped with a closed nondegenerate 2-form. In 2-plectic geometry one finds the higher analogues of many structures familiar from symplectic geometry. For example, any 2-plectic manifold has a Lie 2-algebra consisting of smooth functions and Hamiltonian 1-forms. This is equipped with a Poisson-like bracket which only satisfies the Jacobi identity up to "coherent chain homotopy". Over any 2-plectic manifold is a vector bundle equipped with extra structure called an exact Courant algebroid. This Courant algebroid is the 2-plectic analogue of a transitive Lie algebroid over a symplectic manifold. Its space of global sections also forms a Lie 2-algebra. We show that this Lie 2-algebra contains an important sub-Lie 2-algebra which is isomorphic to the Lie 2-algebra of Hamiltonian 1-forms. Furthermore, we prove that it is quasi-isomorphic to a central extension of the (trivial) Lie 2-algebra of Hamiltonian vector fields, and therefore is the higher analogue of the well-known Kostant-Souriau central extension in symplectic geometry. We interpret all of these results within the context of a categorified prequantization procedure for 2-plectic manifolds. In doing so, we describe how U(1)-gerbes, equipped with a connection and curving, and Courant algebroids are the 2-plectic analogues of principal U(1) bundles equipped with a connection and their associated Atiyah Lie algebroids
Higher U (1)-gerbe connections in geometric prequantization
No full textWe promote geometric prequantization to higher geometry (higher stacks), where a prequantization is given by a higher principal connection (a higher gerbe with connection). We show fairly generally how there is canonically a tower of higher gauge groupoids and Courant groupoids assigned to a higher prequantization, and establish the corresponding Atiyah sequence as an integrated Kostant-Souriau infinity-group extension of higher Hamiltonian symplectomorphisms by higher quantomorphisms. We also exhibit the infinity-group cocycle which classifies this extension and discuss how its restrictions along Hamiltonian infinity-actions yield higher Heisenberg cocycles. In the special case of higher differential geometry over smooth manifolds, we find the L-infinity-algebra extension of Hamiltonian vector fields - which is the higher Poisson bracket of local observables - and show that it is equivalent to the construction proposed by the second author in n-plectic geometry. Finally, we indicate a list of examples of applications of higher prequantization in the extended geometric quantization of local quantum field theories and specifically in string geometry
FIGURE 1. Branchinecta ferrolimneta n in A new species of Branchinecta (Crustacea: Anostraca) from Brasil
No full textFIGURE 1. Branchinecta ferrolimneta n. sp. Male: A) head, anterior view of left side; B) head, lateral view of left side. Female: C) head, anterior view of left side. Scale bar = 1mm.Published as part of Rogers, Christopher & Ferreira, Aloisio, 2007, A new species of Branchinecta (Crustacea: Anostraca) from Brasil, pp. 27-34 in Zootaxa 1445 on page 29, DOI: 10.5281/zenodo.17610
A new species of Branchinecta (Crustacea: Anostraca) with comments on the large branchiopod crustaceans of Kansas
No full textRogers, Christopher, Dasis, Don, Murrow, Daniel G. (2011): A new species of Branchinecta (Crustacea: Anostraca) with comments on the large branchiopod crustaceans of Kansas. Zootaxa 2749: 62-68, DOI: 10.5281/zenodo.20755
A new species of Eulimnadia (Crustacea; Branchiopoda; Diplostraca; Spinicaudata) from North America
No full textRogers, Christopher, Weeks, Stephen C., Hoeh, Walter R. (2010): A new species of Eulimnadia (Crustacea; Branchiopoda; Diplostraca; Spinicaudata) from North America. Zootaxa 2413: 61-68, DOI: 10.5281/zenodo.19432
A version of the Goldman-Millson theorem for filtered L-infinity-algebras
No full textIn this paper we consider L-infinity-algebras equipped with complete descending filtrations. We prove that, under some mild conditions, an L. quasi-isomorphism U : L -> (L) over tilde induces a weak equivalence between the Deligne-Getzler-Hinich (DOE) infinity-groupoids corresponding to L and (L) over tilde, respectively. This paper may be considered as a modest addition to foundational paper [10] by Ezra Getzler. (C) 2015 Elsevier Inc. All rights reserved
L-infinity-ALGEBRAS OF LOCAL OBSERVABLES FROM HIGHER PREQUANTUM BUNDLES
No full textTo any manifold equipped with a higher degree closed form, one can associate an L-infinity-algebra of local observables that generalizes the Poisson algebra of a symplectic manifold. Here, by means of an explicit homotopy equivalence, we interpret this L-infinity-algebra in terms of infinitesimal autoequivalences of higher prequantum bundles. By truncating the connection data on the prequantum bundle, we produce analogues of the (higher) Lie algebras of sections of the Atiyah Lie algebroid and of the Courant Lie 2-algebroid. We also exhibit the L-infinity-cocycle that realizes the L-infinity-algebra of local observables as a Kirillov-Kostant-Souriau-type L-infinity-extension of the Hamiltonian vector fields. When restricted along a Lie algebra action, this yields Heisenberg-like L-infinity-algebras such as the string Lie 2-algebra of semisimple Lie algebra
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