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Titlebook: Lie Theory and Its Applications in Physics; Sofia, Bulgaria, Jun Vladimir Dobrev Conference proceedings 2022 The Editor(s) (if applicable)

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Primordial Black Hole Generation in a Two-Field Inflationary Modele background trajectory in field space. We show that certain classes of solutions to the equations of motion exhibit precisely this kind of behavior. Among them we find solutions, which describe a transition between an ultra-slow roll and a slow roll phases of inflation.
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Levi-Civita Connections on Braided Algebrasnd torsion of arbitrary connections, i.e., not necessarily invariant under the Hopf algebra action. An arbitrary metric tensor defines a unique metric compatible and torsion free connection. The associated Ricci tensor allows to consider in vacuum noncommutative Einstein equations.
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On the Hidden Symmetries of , Supergravityally appearing for consistency of the construction. We also discuss the relation between this hidden superalgebra and other superalgebras of particular relevance in the context of supergravity and superstring, involving a fermionic generator with 32 components.
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