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Coquasi-bialgebroid theory over noncommutative base algebras using Takeuchi coalgebra formalism. Product associative up to invertible normalized 3-cocycle, with twisting theorem by convolution-invertible 2-cochains and Connes-Moscovici-type constructions.
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| name | coquasi-bialgebroids-cocycle-twisting |
| description | Coquasi-bialgebroid theory over noncommutative base algebras using Takeuchi coalgebra formalism. Product associative up to invertible normalized 3-cocycle, with twisting theorem by convolution-invertible 2-cochains and Connes-Moscovici-type constructions. |
Mathematical framework introducing coquasi-bialgebroids over noncommutative base algebras. The coproduct remains an algebra map into the Takeuchi product, while the product is associative only up to an invertible normalized 3-cocycle. Provides a bialgebroid analogue of coquasi-bialgebras and a natural framework for cocycle-twisted bialgebroid constructions, with applications to quantum algebra and noncommutative geometry.
When deforming bialgebroid structures:
When constructing finite group examples:
Coquasi-bialgebroid over B:
Δ: C → C ×_B C (coproduct into Takeuchi product)
μ: C ⊗_B C → C (product, associative up to 3-cocycle)
ε: C → B (counit)
with 3-cocycle ω: C ⊗_B C ⊗_B C → B^×
Given γ: H ⊗ H → B (convolution-invertible 2-cochain):
Δ_γ(c) = γ · Δ(c) · γ⁻¹
ω_γ = δγ · ω
produces new coquasi-bialgebroid structure