LAUSR

Mechanical Structures on Lie Algebroids

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0 Published in 2018 at "Mediterranean Journal of Mathematics"

DOI: 10.1007/s00009-018-1204-y

Abstract: In this paper, we extend the study of mechanical systems in the general framework of Lie algebroids using the associated evolution nonlinear connections. In the case of the prolongations of a Lie algebroid over the… read more here.

Keywords: lie algebroids; structures lie; mechanical structures;

Higher nonabelian omni-Lie algebroids

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0 Published in 2021 at "Journal of Geometry and Physics"

DOI: 10.1016/j.geomphys.2021.104277

Abstract: Abstract In this paper, the structure of higher nonabelian omni-Lie algebroid is studied. The concept of higher nonabelian omni-Lie algebroids on direct sum bundle D E ⊕ ∧ n J E is introduced, and its… read more here.

Keywords: lie algebroids; geometry; lie algebroid; nonabelian omni ... See more keywords

LIE ALGEBROIDS AS $L_{\infty }$ SPACES

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0 Published in 2018 at "Journal of the Institute of Mathematics of Jussieu"

DOI: 10.1017/s1474748018000075

Abstract: In this paper, we relate Lie algebroids to Costello’s version of derived geometry. For instance, we show that each Lie algebroid – and the natural generalization to dg Lie algebroids – provides an (essentially unique)… read more here.

Keywords: lie algebroid; lie algebroids; infty space; infty spaces ... See more keywords

Vanishing theorems on Kähler Lie algebroids

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1 Published in 2020 at "International Journal of Geometric Methods in Modern Physics"

DOI: 10.1142/s0219887820500590

Abstract: In this paper, we extend the Hodge theory to complex Lie algebroids, introduce the Laplacian operators and decompose the cohomological groups with respect to these operators, and generalize Kahler ... read more here.

Keywords: lie algebroids; theorems hler; vanishing theorems; hler lie ... See more keywords

Equivalent Description of Hom-Lie Algebroids

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0 Published in 2018 at "Advances in Mathematical Physics"

DOI: 10.1155/2018/8417516

Abstract: We study representations of Hom-Lie algebroids, give some properties of Hom-Lie algebroids, and discuss equivalent statements of Hom-Lie algebroids. Then, we prove that two known definitions of Hom-Lie algebroids can be transformed into each other… read more here.

Keywords: lie algebroids; hom lie; description hom; equivalent description ... See more keywords