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On the boundary Carrollian conformal algebra
Lucas Buzaglo1, Xiao He2, Tuan Anh Pham3
1Department of Mathematics, UC San Diego, La Jolla, CA 92093-0112 USA.
Letters in Mathematical Physics
|July 23, 2026
Summary
This study introduces the boundary Carrollian conformal algebra (BCCA), a novel Lie algebra. Researchers developed new modules and irreducibility criteria for BCCA and its subalgebra O, advancing Carrollian physics and representation theory.
Area of Science:
- Mathematics
- Theoretical Physics
Background:
- The boundary Carrollian conformal algebra (BCCA) is a recently discovered infinite-dimensional Lie algebra with unique filtered but not graded properties.
- Carrollian physics and representation theory present intriguing mathematical structures.
Purpose of the Study:
- To initiate the mathematical study of the boundary Carrollian conformal algebra (BCCA).
- To construct modules for the BCCA and its subalgebra O.
- To establish irreducibility criteria for these modules.
Main Methods:
- Restriction of known modules from BMS3 and Witt algebras to construct BCCA modules.
- Proving irreducibility criteria for BMS3 massive modules and comparing them to Verma modules.
- Developing intrinsic module constructions for BCCA using a new basis and filtration.
Main Results:
- Established that BMS3 massive modules share irreducibility criteria with Verma modules.
- Demonstrated that BCCA actions on massive module generating vectors are irreducible under the same criteria.
- Constructed Whittaker modules over BCCA and subalgebra O, proving their irreducibility criteria.
Conclusions:
- The study provides a foundational mathematical framework for the BCCA.
- New insights into module theory for Carrollian physics and related algebras are presented.
- The developed criteria offer a pathway for further representation-theoretic investigations of the BCCA.
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