On Higher Frobenius-Schur Indicators.

Intro -- Contents -- Introduction -- Chapter 1. The Calculus of Sweedler Powers -- 1.1. Monotone maps -- 1.2. The union of the symmetric groups -- 1.3. Bialgebras -- 1.4. A monoid -- 1.5. Permutations from sequences -- 1.6. Sweedler powers -- Chapter 2. Frobenius-Schur Indicators -- 2.1. Central Sweedler powers -- 2.2. The coproduct of the Sweedler powers -- 2.3. The first formula for the Frobenius-Schur indicators -- 2.4. The Frobenius-Schur theorem -- 2.5. Frobenius-Schur indicators of the regular representation -- Chapter 3. The Exponent -- 3.1. The exponent -- 3.2. The second formula for the Frobenius-Schur indicators -- 3.3. Sweedler powers of the integral -- 3.4. Cauchy's theorem -- Chapter 4. The Order -- 4.1. Order and multiplicity -- 4.2. The divisibility theorem -- 4.3. An example -- 4.4. The dimension of the simple modules -- Chapter 5. The Index -- 5.1. Indecomposable matrices -- 5.2. The normal form -- 5.3. The Perron-Frobenius theorem -- 5.4. The index formula -- Chapter 6. The Drinfel'd Double -- 6.1. The Drinfel'd double -- 6.2. Factorizability -- 6.3. The center of the character ring -- 6.4. The third formula for the Frobenius-Schur indicators -- Chapter 7. Examples -- 7.1. A class of extensions -- 7.2. The coefficients -- 7.3. Sweedler powers of the integral -- 7.4. The simple modules -- 7.5. Nonintegral indicators -- 7.6. Noncocommutative Sweedler powers -- 7.7. Noncentral Sweedler powers -- Bibliography -- Subject Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- L -- M -- N -- O -- P -- R -- S -- T -- U -- V -- W -- Symbol Index.

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