mathematics

Moss Sweedler

Moss Sweedler is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Moss Sweedler rather than just read about it. In short: Moss Eisenberg Sweedler (born 29 April 1942, in Brooklyn) is an American mathematician, known for Sweedler's Hopf algebra, Sweedler's notation, measuring coalgebras, and his proof, with Harry Prince Allen, of a conjecture of Nathan Jacobson. Education and career Sweedler received his Ph.D. from the Massachusetts Institute of Technology in 1965.

Key takeaways

Moss Sweedler belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Moss Sweedler to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Moss Sweedler from memory before moving on to harder problems.

Reference excerpt

Moss Eisenberg Sweedler (born 29 April 1942, in Brooklyn) is an American mathematician, known for Sweedler's Hopf algebra, Sweedler's notation, measuring coalgebras, and his proof, with Harry Prince Allen, of a conjecture of Nathan Jacobson.

Education and career Sweedler received his Ph.D. from the Massachusetts Institute of Technology in 1965. His thesis, Commutative Hopf Algebras with Antipode, was written under the direction of thesis advisor Bertram Kostant. Sweedler wrote Hopf Algebras (1969), which became the standard reference book on Hopf algebras. He, with Harry P. Allen, used Hopf algebras to prove in 1969 a famous 25-year-old conjecture of Jacobson about the forms of generalized Witt algebras over algebraically closed fields of finite characteristic. From 1965 to the mid 1980s Sweeder worked on commutative algebra and related disciplines. Since the mid 1980s Sweedler has worked primarily on computer algebra. His research resulted in his position as director of the Army Center of Excellence for computer algebra. Sweedler was an Invited Speaker at the International Congress of Mathematicians in 1974 in Vancouver. He was a Guggenheim Fellow for the academic year 1980–1981. With his wife Kristin, he helped establish the Sweedler Nature Preserve.

Selected publications Sweedler, Moss Eisenberg (1967). "Hopf algebras with one grouplike element". Trans. Amer. Math. Soc. 127 (3): 515–526. doi:10.1090/s0002-9947-1967-0210748-5. MR 0210748. Sweedler, Moss E. (1967). "Cocommutative Hopf algebras with antipode". Bull. Amer. Math. Soc. 73 (1): 126–128. doi:10.1090/s0002-9904-1967-11677-x. hdl:1721.1/72926. MR 0214646. Sweedler, Moss Eisenberg (1968). "Cohomology of algebras over Hopf algebras". Trans. Amer. Math. Soc. 133: 205–239. doi:10.1090/s0002-9947-1968-0224684-2. MR 0224684. Sweedler, Moss E. (1969), Hopf algebras, Mathematics Lecture Note Series, W. A. Benjamin, Inc., New York, ISBN 9780805392548, MR 0252485 with H. P. Allen: Allen, Harry Prince; Sweedler, Moss Eisenberg (1969). "A theory of linear descent based upon Hopf algebraic techniques". J. Algebra. 12 (2): 242–294. doi:10.1016/0021-8693(69)90051-9. MR 0242906. with Richard G. Larson: Larson, Richard Gustavus; Sweedler, Moss Eisenberg (1969). "An associative orthogonal bilinear form for Hopf algebras". Amer. J. Math. 91 (1): 75–94. doi:10.2307/2373270. JSTOR 2373270. Sweedler, Moss E. (1971). "Weakening a theorem on divided powers". Trans. Amer. Math. Soc. 154: 427–428. doi:10.1090/s0002-9947-1971-0279162-1. MR 0279162. Groups of simple algebras, Institut des Hautes Etudes Scientifiques 44 (1975), 79–189. Sweedler, Moss (1975). "The predual theorem to the Jacobson-Bourbaki theorem". Trans. Amer. Math. Soc. 213: 391–406. doi:10.1090/s0002-9947-1975-0387345-9. MR 0387345. Sweedler, Moss Eisenberg (1975). "When is the tensor product of algebras local?". Proc. Amer. Math. Soc. 48: 8–10. doi:10.1090/s0002-9939-1975-0360568-6. MR 0360568. with Kenneth Newman: Newman, Kenneth; Sweedler, Moss E. (1979). "A realization of the additive Witt group". Proc. Amer. Math. Soc. 76 (1): 39–42. doi:10.1090/s0002-9939-1979-0534386-3. MR 0534386. with Darrell E. Halle and R. Larson: Haile, Darrell E.; Larson, Richard G.; Sweedler, Moss E. (1983). "A new invariant for C over R: almost invertible cohomology theory and the classification of idempotent cohomology classes and algebras by partially ordered sets with a Galois group action". Amer. J. Math. 105 (3): 689–814. doi:10.2307/2374320. JSTOR 2374320. with I. Rubio and C. Heegard: Gröbner bases for linear recursion relations on m-D arrays and applications to decoding, Proc. IEEE Int'l Symp. on Information Theory, June 29–July 4, 1997, Ulm, Germany. with K. Shirayanagi: Remarks on automatic algorithm stabilization, invited contribution to (fourth) IMACS Conf. on Appl. of Computer Algebra (1998). with L. Robbiano: Robbiano, Lorenzo; Sweedler, Moss (1998). "Ideal and subalgebra coefficients". Proc. Amer. Math. Soc. 126 (8): 2213–2219. doi:10.1090/s0002-9939-98-04306-8. MR 1443407. with Edward Mosteig: Mosteig, Edward; Sweedler, Moss (2004). "The growth of valuations on rational function fields in two variables". Proc. Amer. Math. Soc. 132 (12): 3473–3483. doi:10.1090/s0002-9939-04-07456-8. MR 2084067.

References

Worked examples

Example 1 — a first encounter with Moss Sweedler

Start with the simplest possible case. Write down what Moss Sweedler claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Moss Sweedler before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Moss Sweedler ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Moss Sweedler

In research: Moss Sweedler appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Moss Sweedler in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Moss Sweedler is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1942 births, 20th-century American mathematicians, 21st-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Moss Sweedler outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Moss Sweedler in 20 minutes

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Frequently asked questions

What is Moss Sweedler in simple terms?

Why does Moss Sweedler matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Moss Sweedler?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Moss Sweedler.