mathematics

Jean-Louis Loday

Jean-Louis Loday 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 Jean-Louis Loday rather than just read about it. In short: Jean-Louis Loday (12 January 1946 – 6 June 2012) was a French mathematician who worked on cyclic homology and who introduced Leibniz algebras (sometimes called Loday algebras) and Zinbiel algebras. He occasionally used the pseudonym Guillaume William Zinbiel, formed by reversing the last name of Gottfried Wilhelm Leibniz.

Key takeaways

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

Reference excerpt

Jean-Louis Loday (12 January 1946 – 6 June 2012) was a French mathematician who worked on cyclic homology and who introduced Leibniz algebras (sometimes called Loday algebras) and Zinbiel algebras. He occasionally used the pseudonym Guillaume William Zinbiel, formed by reversing the last name of Gottfried Wilhelm Leibniz.

Education and career Loday studied at Lycée Louis-le-Grand and at École Normale Supérieure in Paris. He completed his Ph.D. at the University of Strasbourg in 1975 under the supervision of Max Karoubi, with a dissertation titled K-Théorie algébrique et représentations de groupes. He went on to become a senior scientist at CNRS and a member of the Institute for Advanced Mathematical Research (IRMA) at the University of Strasbourg.

Publications

Loday, Jean-Louis (1998), Cyclic homology, Grundlehren der Mathematischen Wissenschaften, vol. 301 (2nd ed.), Berlin, New York: Springer-Verlag, ISBN 978-3-540-63074-6, MR 1600246 Loday, Jean-Louis & Pirashvili, Teimuraz (1993). "Universal enveloping algebras of Leibniz algebras and (co)homology". Mathematische Annalen. 296 (1): 139–158. CiteSeerX 10.1.1.298.1142. doi:10.1007/BF01445099. S2CID 16865683. {{cite journal}}: Cite uses deprecated parameter |citeseerx= (help) Loday, Jean-Louis; Vallette, Bruno (2012), Algebraic Operads (PDF), Grundlehren der Mathematischen Wissenschaften, vol. 346, Berlin, New York: Springer-Verlag, ISBN 978-3-642-30361-6, archived from the original (PDF) on 2011-08-23, retrieved 2012-06-20 Zinbiel, Guillaume William (2012), "Encyclopedia of types of algebras 2010", in Guo, Li; Bai, Chengming; Loday, Jean-Louis (eds.), Operads and universal algebra, Nankai Series in Pure, Applied Mathematics and Theoretical Physics, vol. 9, pp. 217–298, arXiv:1101.0267, Bibcode:2011arXiv1101.0267Z, ISBN 9789814365116, Zinbiel is a pseudonym of Jean-Louis Loday

See also Associahedron Blakers–Massey theorem Loday functor

References

Obituary Home page Archived 2017-07-04 at the Wayback Machine Jean-Louis Loday at the Mathematics Genealogy Project

External links Loday's biography of Guillaume William Zinbiel Archived 2011-08-23 at the Wayback Machine

Worked examples

Example 1 — a first encounter with Jean-Louis Loday

Start with the simplest possible case. Write down what Jean-Louis Loday 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 Jean-Louis Loday 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 Jean-Louis Loday 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 Jean-Louis Loday

In research: Jean-Louis Loday 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 Jean-Louis Loday 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: Jean-Louis Loday is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1946 births, 2012 deaths, 20th-century French mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Jean-Louis Loday 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 Jean-Louis Loday in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Jean-Louis Loday means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Jean-Louis Loday out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Jean-Louis Loday in simple terms?

Why does Jean-Louis Loday 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 Jean-Louis Loday?

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 Jean-Louis Loday.