nLab Jacob Towber

Jacob Towber was an American algebraist with tenure at de Paul University at Chicago. An example of finite dimensional noncommutative Hopf algebras is named after him (Radford’s Hopf algebras) with most famous member in dimension 8. The purpose of his example originally was to give an example of a Hopf algebra whose Jacobson radical is not a Hopf ideal.

Selected works

Radford’s Hopf algebras were exhibited in

• D. E. Radford, On the coradical of a finite-dimensional Hopf algebra Proc. Am. Math. Soc. 53 (1975) 9–15 MR2197389 doi

Material on functors with Young symmetry (related to invariant theory, Schur functors, flag varieties and so on)

• Jacob Towber, Two new functors from modules to algebras, J. Algebra 47, 80–104 (1977) pdf
• Jacob Towber, Young symmetry, the flag manifold, and representations of GL(n), J. Alg. 61, 414–462 (1979)
• Glenn Lancaster, Jacob Towber, Representation-functors and flag-algebras for the classical groups I, J. Alg. 59, 16–38 (1979) pdf

On Yetter-Drinfeld modules

• David E. Radford, Jacob Towber, Yetter–Drinfel’d categories associated to an arbitrary bialgebra, J. Pure Appl. Algebra 87 (1993), 259–279 MR94f:16060 doi

On quantum Grassmannians and quantum flag varieties

• Earl Taft, Jacob Towber, Quantum deformation of flag schemes and Grassmann schemes $q$-deformation of the shape-algebra for $GL(n)$, J. Algebra 142 (1991) 1-36 doi

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