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A family of Whittaker modules over the universal central extension of the planar Galilean conformal algebra can be constructed, with established necessary and sufficient conditions for their irreducibility and determined isomorphism classes for their tensor product modules. Novelty: ClaimNovelty.INCREMENTAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

August 24, 2026Mathematische NachrichtenOpen Access

Irreducible Modules Over the Universal Central Extension of the Planar Galilean Conformal Algebra

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To investigate the representation theory of the universal central extension of the planar Galilean conformal algebra by classifying irreducible Whittaker and tensor product modules.
Constructed a family of Whittaker modules over the universal central extension of the planar Galilean conformal algebra.
Formulated tensor product modules combining rank-one free modules over polynomial subalgebras with irreducible restricted modules.
Derived algebraic conditions to classify module irreducibility and establish isomorphism classes.
Obtained necessary and sufficient conditions for the irreducibility of Whittaker modules when structural indices share the same parity.
Established definitive irreducibility criteria for the constructed tensor product modules.
Determined and classified all isomorphism classes for the tensor product representations.

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Implication

Theoretical algebraic analysis determines irreducibility criteria and isomorphism classes for representations, advancing understanding of planar Galilean conformal symmetry structures.

Cite This Study

Dongfang Gao (2026) studied this question.

synapsesocial.com/papers/6a8c0010bca056c88e6dee67 https://doi.org/10.1002/mana.70246

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Implication

Theoretical algebraic analysis determines irreducibility criteria and isomorphism classes for representations, advancing understanding of planar Galilean conformal symmetry structures.

Irreducible Modules Over the Universal Central Extension of the Planar Galilean Conformal Algebra

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Implication

Cite This Study

Irreducible Modules Over the Universal Central Extension of the Planar Galilean Conformal Algebra

Key Points

Discussion

Implication

Cite This Study

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