⊕_{k≥0} V^{⊗k}, the free associative algebra on V. Universal: any linear map V → A to an associative algebra A extends uniquely to an algebra map T(V) → A.
Tensor algebra T(V)
Related concepts
- Tensor product V ⊗ W
- Universal property
- Tensor decomposition
- Hopf algebra
- Module over a ring
- Lie algebra & bracket
- Malcev algebra
- Induced representation + Frobenius reciprocity
- Tannakian formalism
- Quantum groups (Drinfeld-Jimbo)
- Modular tensor category (CFT)
- Linear logic (Girard)
- Nusselt-Rayleigh scaling law: Nu = C_N * Ra^{1/3} for high-Ra turbulent Rayleigh-Benard convection
- Continuum mechanics
- SUSY algebra (graded Lie)
- Superspace + superfield
- Deformed special relativity
- Turbulence ML models
- Riemannian metric tensor (physics)
- Primary fields + conformal weights