Divisible homology classes in the special linear group of a number eld

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• cours magistral - matière potentielle : notes
• cours magistral - matière potentielle : note ser

Divisible homology classes in the special linear group of a number eld Dominique Arlettaz and Piotr Zelewski Introduction Let F be a number eld and SL(F ) denote the innite special linear group over F . The integral homology groups of SL(F ) are in general not nitely generated but, it was shown by the rst author in Section 2 of [A1] that, for all integers i 0 , Hi(SL(F );Z) is the direct sum of a free abelian group of nite rank and a torsion group.

• wedge of eilenberg-maclane spectra
• iterated homology suspension
• torsion group
• nite group
• mention that the structure of the integral homology groups
• product of eilenberg
• divisible homology classes
• image
• sl
• groups

Sujets

• Lausanne
• Cambridge University
• Homology
• Intégral
• Eilenberg
• Group

Informations

• Publié par: odwo
• Nombre de lectures: 32
• Langue: English

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1Medieval Wisdom Literature and the “Circle of Justice”

Draft Only. Please Do Not Cite or Circulate.

Jennifer London
University of Chicago
Fall, 2007

Comments are welcome: [e-mail]

Key Words: Wisdom, Wisdom Literature, the “Circle of Justice,” Persian Political Thought,
Arabic Political Thought, History of Political thought, Language and Politics.


Introduction
One of the best tools we have for learning about modern political thought, and for differentiating
it from what is ancient, is to look to how modern scholars invoked the past to express their
2concerns about the present. In this way, Benjamin Constant (1830/1246) and Hannah Arendt
(1974/1395) transported us to ancient Athens, where politics was as it should be, to show us how
far we have fallen. Likewise, we can learn about medieval Islamic political thought by
considering how medieval Arab and Persian kings, ministers and scholars recited sayings from
ancient Greece and Persia. When we look at how these medieval speakers articulated variations
of two popular sayings, sayings that contemporary scholars call the “circle of justice,” we find an
ideal form of political organization that speakers associated with political order and stability and
wished to import into their current environments.
In practical terms, Arab and Persian princes, ministers and intellectuals invoked sayings
that they attributed to ancient Greeks, Persians and Indians in order to advise princes.
Collections of these sayings are called “ ikma” or “wisdom literature.” As political figures
invoked these sayings in distinct medieval Islamic contexts, in Persian, Arabic and Turkish, they
continued pre-existing conversations about political thought (e.g., how to organize society to
insure economic prosperity, social order and peace) in new contexts. In this chapter, I interpret

1 Thanks very much to John Woods, Danielle Allen, Joe Yackley, Jenna Jordan and Leigh Jenco for
comments on an earlier version of this paper. Special thanks to Aram Shahin for weeks of discussions on these texts
and for advising me on sources.
2 For each person mentioned in this dissertation, I write the year of their death in the western calendar
followed by that year in the Islamic calendar. ­
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two sayings to observe what they might teach us about medieval Arabic and Persian political
thought. These sayings represent models for how to achieve political stability that kings,
ministers and scholars sought to implement in different ways. My purpose is to learn what
authors might have achieved politically by invoking political wisdom from another context, and
how such invocations enabled elite speakers to advocate a hierarchical vision of social order and
justice that served their interests.
Medieval Arab and Persian kings, ministers and historians invoked two popular sayings
that they attributed to the Greek philosopher Aristotle (322 BCE) and to Ardash īr (ruled 224-241
3CE), the founder of the Persian Sasanian dynasty. While the narrative forms of these sayings
differ slightly, both emphasize the ways that leaders ought to organize society to facilitate
political stability, order and economic prosperity. These two sayings represent an ideology for
4an agrarian economy. They are part of the genres of wisdom literature and of the mirror for
5princes tradition, as they represent wisdom ( ikma) attributed to sages in other cultural contexts,
and medieval scholars incorporate these sayings into works they write to educate princes. They
read,
6The world is a garden (bust ān) ,
7and the fence of it is the dynasty (dawla) ;
The dynasty is authority (sulÔ ān),
and through it customs (sunna) are kept alive;
The customs (sunna) are a way of governing (siy āsa),
that is implemented by the sovereign (malik);
The sovereign (malik) is a shepherd (r ā‘i),
and the soldiers (jaysh) help him;
The soldiers are helpers,
and money provides for them;
Money is livelihood (rizq),
that the flock (ra‘Ðya) gather;

3 Ardash īr was the ruler of Persia (224-241 CE) and the founder of the Sasanian dynasty (226–651 CE).
4 L. Darling, 2002, “Do Justice, Do Justice, For That is Paradise,” Comparative Studies of South Asia, Africa
and the Middle East 22.1-2 (2002), p. 2.
5 The word wisdom ( ikma) connotes an Arabic tradition of Greek, Persian and Indian sayings in
translation that introduce morals about social and political life from other contexts. Analogous to the Greek
gnomologic genre, the sayings that constitute this tradition are scattered and are thus difficult to study in a
systematic way. For an introduction to Arabic gnomologia see Dimitri Gutas’ “Classical Arabic Wisdom Literature:
Nature and Scope” Journal of the American Oriental Society Vol. 10 (1981), pp. 49-86. See also Gutas’ work Greek
Wisdom Literature in Arabic Translation (New Haven, 1975).
6 A bust ān is “a garden of sweet scented flowers and trees” but according to Arabic lexicons it is associated
with the garden of heaven (janna) (See E.W. Lane, Arabic-English Lexicon, Part I (London, 1863-1893), p. 202.
7 While dawla in this context means dynasty, it comes from the root “dwl” which means to turn, and is
linked with the turning of fortune from and unhappy state to a good and happy one (See E.W. Lane, Arabic-English
Lexicon, Part I, p. 934). The term dawla can also mean the turning of fortune’s wheel.
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The flock are slaves,
devoted to the service of (yata‘abbaduhum) justice (‘adl);
Justice is a norm,
and it is alive in the world;
8-Attributed to Aristotle

There is no authority (sulÔ ān) without men,
and there are no men (rij āl) without money,
and there is no money without cultivation (‘im āra),
and there is no cultivation without justice and good governance
9( usn siy āsa)
-Attributed to Ardash īr

These sayings reveal a vision of political stability that results from keeping social
“estates” (namely farmers, soldiers, tax collectors and the sovereign) localized to their respective
10planes. When speakers recited these sayings they also suggested that the welfare of the various
social groups depended upon one another and that the king and his employees were to insure that
11no group was oppressed by other groups.

8 We find this saying in a text attributed to Aristotle, Kit āb Sirr al-Asr ār (The Book of the Secret of Secrets).
This book is of dubious authenticity. Supposedly, it was a letter that Aristotle wrote to Alexander, as the teacher was
too old to follow his student on his campaign to Persia. There is an Arabic version of the text attributed to the ninth
century Arabic translator Ya y ā ibn al-BiÔr īq (d. c. 800/184), a translator of works of Greek into Arabic (see Ibn al-
Nad īm’s Fihrist, Dodge, tr., (New York, 1970), p. 586). Contemporary scholars, however, consider this treatise
apocryphal and believe that it was written in Arabic in the tenth century. See M. Manzalaoui, Secretum Secretorum:
Nine English Versions. Vol. I. (Oxford, 1977), Introduction. See also the introduction to the book edited by ‘Abd al-
Ra mÁn BadawÐ, al-U ūl al-y ūn ān īya lil-naÛar īya al-siy ās īya f ī al-Isl ām (Cairo, 1954). Badawi believes that those
reading the text in the tenth century thought it was by Aristotle (see his introduction to the text just mentioned in
Arabic). In this chapter, I rely on BadawÐ’s Arabic edition, cited above, of the Kit āb Sirr al-Asr ār (The Book of the
Secret of Secrets), drawn from later Arabic manuscripts (the oldest of which is from the fourteenth century). I
concentrate on the part of the text that corresponds with Aristotle’s letter to Alexander on the image of justice (which
in this edition is called “section three” (al-maq āla al-th ālitha), “on the form of justice” (f ī ūrat al-‘adl), pp. 125-128).
9 We find this saying attributed to Ardash īr in ‘Ahd Ardash īr I s ān ‘Abb ās ed. (Beirut, 1967), p. 98. It is
located in the second part of ‘Abb ās’ edition entitled “Scattered Sayings of Ardash īr.” The editor implies that these
sayings were popular in Arabic at the time the work ‘Ahd Ardash īr was translated into Arabic. We can assume that
literature that contains this saying enters the Islamic tradition in the late Umayyad period (661-750/40-132) through
translations of texts like ‘Ahd Ardash īr. See J. “The Last Days of al-Ghazz āl ī and the Tripartite Division of the Sufi
World.” The Muslim World. Vol. 96 (January 2006), p. 96. I s ān ‘Abb ās claims that the text ‘Ahd Ardash īr, a
corpus of Ardash īr’s political wisdom, existed in Arabic by the middle of the eighth-century (see the introduction to
‘Abb ās ed. of ‘Ahd Ardash īr, 1967, also sited in J. Brown, “The Last Days of al-GhazzÁlД p. 108, ft., 16).
10 See A. Lambton, “Justice in the Medieval Persian Theory of Kingship” Studia Islamica, 17 (1962), pp.
91-119; See also H. Yucesoy’s article “Political Theory”, Vol. 2, pp. 623-628, Medieval Islamic Civilization: An
Encyclopedia